id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,170 | AMR-117-0018 | Moments of L-functions — Moments of the Riemann zeta function — Problem 20 | Remove the integral in $t$ from Chandee-Li's work and give an asymptotic formula for
$$
\frac{2}{\phi(q)} \sum_{\substack{\chi \mod{q}\\ \chi(-1)=(-1)^k}} \sum_{f\in\mathcal{H}_\chi}^h \left|L\left({\textstyle \frac{1}{2}},f\right)\right|^6
$$
See work of Chandee-Li-Matomaki-Radziwill on the sixth moment of Dirichlet $... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 20
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,171 | AMR-117-0019 | Moments of L-functions — Moments of the Riemann zeta function — Problem 21 | Consider the family of Rankin-Selberg $L$-functions $L(\frac12,f\otimes g)$ where $g$ is fixed and $f$ varies over the set of primitive forms of weight $k$ and level $p^{\nu}$ as $\nu\to\infty$. Establish upper bounds for third and fourth moments of this family following the work in [ChL1] and [ChL2].
Note that the 4th... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 21
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,172 | AMR-117-0020 | Moments of L-functions — Moments of the Riemann zeta function — Problem 23 | Determine a polynomial $P$ of degree 10 such that
\begin{equation}
\sum_{0 < d < X} L(\tfrac{1}{2}, \chi_{8d})^4 = X P(\log X) + o(X)
\end{equation}
where $d$ ranges through odd square-free numbers and $\chi_{8d}$ denotes the quadratic character associated to the fundamental discriminant $8d$.
Can the error term $o(X)... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 23
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,173 | AMR-117-0021 | Moments of L-functions — Moments of the Riemann zeta function — Problem 24 | Shen and Stucky [ShSt] have determined the first four coefficients of this polynomial. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 24
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,174 | AMR-117-0022 | Moments of L-functions — Moments of the Riemann zeta function — Problem 25 | Compute moments for families of Artin-Schreier $L$-functions and improve results on 1-level zero density.\\
Notation: $p>2$ prime, $q$ power of $p$, $\mathcal{L}(u,f,\psi)$ is the Artin-Schreier $L$-function
associated with rational function $f\in\mathbb{F}_q(x)$ and additive character $\psi$,
$$\mathcal{AS}^0_d=\{f\in... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 25
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,175 | AMR-117-0023 | Moments of L-functions — Moments of the Riemann zeta function — Problem 26 | Investigate the dependence of zero-density on moments of the zeta-function? More specifically, Ingham’s zero-density estimate makes use of the fourth moment $\int_{T}^{2T} |\zeta(1/2 + it)|^{4} dt$. Can we use other non-trivial moments (like, say, Heath-Brown’s estimate of the 12th moment) in such zero-density results,... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 26
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,176 | AMR-117-0024 | Moments of L-functions — Moments of the Riemann zeta function — Problem 27 | Chandee and Soundararajan [CS] proved that the Riemann Hypothesis implies
\[
|\zeta(\tfrac{1}{2}+it)|
\ll \exp \left( (C_0 +o(1)) \frac{\log t}{\log \log t} \right)
\]
with $C_0 = \frac{\log 2}{2}= 0.1505 \ldots $. Reduce the value of $C_0$. \\
(N. Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 27
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,177 | AMR-117-0025 | Moments of L-functions — Moments of the Riemann zeta function — Problem 28 | Let $S(t)=\frac{1}{\pi} \arg \zeta(\tfrac{1}{2}+it)$. Carneiro, Chandee, and Milinovich [CCM] proved that the Riemann hypothesis
implies
\[
|S(t)| \le (C_0+o(1)) \cdot \frac{ \log t}{\log \log t}
\]
with $C_0 =\frac{1}{4}$. Reduce the value of $C_0$. \\
(Nathan Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 28
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,178 | AMR-117-0026 | Moments of L-functions — Moments of the Riemann zeta function — Problem 29 | Let $f$ be a Hecke--Maass cusp form of level 1. Prove the Weyl-strength subconvex bound $L(1/2+it,f) \ll_{\varepsilon} ((1 + |t_f - t|)(1 + |t_f + t|))^{1/6 + \varepsilon}$. This is known, via work of Jutila and Motohashi, for all $t \in \mathbb{R}$ away from the conductor-dropping regimes, namely when either $t_f - t$... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 29
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,179 | AMR-117-0027 | Moments of L-functions — Moments of the Riemann zeta function — Problem 30 | Topacogullari [T1], [T3] and Drappeau [Dr] have proven asymptotic formulae for $D_{k,2}(x,h)$.
Prove an omega theorem for $D_{k,2}(x,h)-M_{k,2}(x,h)$ for $k \ge 3$ where $M_{k,2}(x,h)$ is the main term in the asymptotic formula. \\
(N. Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 30
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,180 | AMR-117-0028 | Moments of L-functions — Moments of the Riemann zeta function — Problem 31 | Topacogullari [T1] proved that for $1 \le h \ll x^{\frac{2}{3}}$
\[
D_{3,2}(x,h) = x P_3(\log x) + O(x^{\frac{8}{9}+\varepsilon})
\]
for a certain degree 3 polynomial where the coefficients of $P_3$ depend on $h$. A result was also obtained for $D_{2,3}(x,h)$. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 31
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,181 | AMR-117-0029 | Moments of L-functions — Moments of the Riemann zeta function — Problem 32 | Improve the range of $h$ and the size of the error term. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 32
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,182 | AMR-117-0030 | Moments of L-functions — Moments of the Riemann zeta function — Problem 33 | Compute exact simple formulae for the coefficients of $P_3$. Numerically check the size of $| D_{3,2}(x,h) - x P_3(\log x)| $.
Is the error term of size $\sqrt{x}$? See the recent related article of Nguyen [Nguyen].
(Nathan Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,183 | AMR-117-0031 | Moments of L-functions — Moments of the Riemann zeta function — Problem 35 | Asymptotically evaluate
\[
\sum_{n \le x} d_3(n) d_3(n+1).
\]
(folklore) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,184 | AMR-117-0032 | Moments of L-functions — Moments of the Riemann zeta function — Problem 36 | Asymptotically evaluate
\[
\sum_{n \le x} d(n) d(n+1) d(n+2).
\]
(folklore) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,185 | AMR-117-0033 | Moments of L-functions — Moments of the Riemann zeta function — Problem 37 | Let $\kappa \in (0,1)$. Asymptotically evaluate
\[
\sum_{n \le x} d_{\kappa}(n) d(n+1) d(n+2).
\] | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 37
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,186 | AMR-117-0034 | Moments of L-functions — Moments of the Riemann zeta function — Problem 38 | Let $\kappa \in (2,3)$. Asymptotically evaluate
\[
\sum_{n \le x} d_{\kappa}(n) d_3(n+1).
\] | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 38
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,187 | AMR-117-0035 | Moments of L-functions — Moments of the Riemann zeta function — Problem 39 | Find a (conjectural) asymptotic formula for
\[
\sum_{n \le x} d_{k_1}(n+h_1) d_{k_2}(n+h_2) \cdots d_{k_r}(n+h_r)
\]
where $(k_1, \ldots, k_r) \in \mathbb{N}^r$ and $h_1, \ldots, h_r$ are distinct positive integers with $r \ge 3$.
This would be analogous to the. conjectural asymptotic formula for
\[
\sum_{n \le x} \Lam... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 39
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,188 | AMR-117-0036 | Moments of L-functions — Moments of the Riemann zeta function — Problem 40 | Let $k \in \mathbb{N}$ and $k \ge 3$.
For some small $\epsilon_0\geq0$ asymptotically evaluate
\[
\int_{0}^{T} \sum_{m \le T^{2+\epsilon_0}} \frac{d_k(m)}{m^{\frac{1}{2}+it}}
\sum_{n \le T^{2+\epsilon_0}} \frac{d(n)}{n^{\frac{1}{2}-it}} dt.
\]
Note that for mean values of long Dirichlet polynomials we know how to evalu... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 40
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,189 | AMR-117-0037 | Moments of L-functions — Moments of the Riemann zeta function — Problem 41 | Let $g$ be a primitive cusp form of weight $k$ for $\Gamma_{0}(N)$. Assume that $g$ is arithmetically normalized so that its first Fourier coefficient $a_g(1)=1$ and write $g(z)=\sum_{n=0}^{\infty}\lambda_{g}(n)n^{\frac{k-1}{2}}e(nz)$. Let $X, Y, P\geq 1$, and let $F(x,y)$ be a smooth weight function supported on $(X/4... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 41
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,190 | AMR-117-0038 | Moments of L-functions — Moments of the Riemann zeta function — Problem 42 | Determine the dependence of the explicit constant on $k$ and $N$. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 42
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,191 | AMR-117-0039 | Moments of L-functions — Moments of the Riemann zeta function — Problem 43 | For a primitive cusp form $g$ of weight $k$ for the full modular group, establish an asymptotic upper bound that is uniform in the weight aspect. Such bounds are useful in moment computations for Rankin-Selberg $L$-functions associated with primitive forms of varying large weights.
(A. Hamieh, UNBC) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 43
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,192 | AMR-118-0001 | Holomorphic Symplectic Geometry — Question 1 | In the two last examples it would seem simpler to start with a moduli space $\mathcal{M}$ for which the natural compactification $\overline{\mathcal{M}}$ is smooth; in that case $\overline{\mathcal{M}}$ is a hyperk\"ahler manifold [M], but it turns out that it is a deformation of $S^{[r]}$ or $K_r(T)$ (G\"ottsche-Huybr... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 1
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,193 | AMR-118-0002 | Holomorphic Symplectic Geometry — Question 2 | Let $X$, $X'$ be two hyperk\"ahler manifolds of the same dimension. If there is a Hodge isometry $\lambda :H^2(X,\mathbb{Z})\vbox{\hbox to .8cm{\hfill{$\scriptstyle\sim$}\hfill}
\nointerlineskip\hbox to .8cm{{\hfill$\longrightarrow $\hfill}} } H^2(X',\mathbb{Z})$, what can we say of $X$ and $X'$? Can we conclude that $... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 2
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,194 | AMR-118-0003 | Holomorphic Symplectic Geometry — Question 3 | Thus the subalgebra $\mathcal{H}$ is completely determined by the form $q$ and the dimension of $X$. In contrast, not much is known about the $\mathcal{H}$-module $\mathcal{H}^\perp$. Note that it is nonzero for the examples $a)$ and $b)$ of 1.2, with the exception of $S^{[2]}$ for a K3 surface $S$.
We do not know much... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 3
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,195 | AMR-118-0004 | Holomorphic Symplectic Geometry — Conjecture 4 | Having so few examples leads naturally to the following question:
There are finitely many hyperk\"ahler manifolds (up to deformation) in each dimension. | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 4
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,196 | AMR-118-0005 | Holomorphic Symplectic Geometry — Question 5 | Note that $b_2$ is $23$ for $S^{[2]}$ and $7$ for $K_2(T)$ (1.2).
[G] contains some more information on the other Betti numbers.
Can we exclude some more cases, in particular $b_2=3$? If $b_2=23$, can we conclude that $X$ is deformation equivalent to $S^{[2]}$? | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 5
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,197 | AMR-118-0006 | Holomorphic Symplectic Geometry — Conjecture 6 | \mathrm{a)} Let $L$ be a nontrivial nef line bundle on $X$ with $q(L)=0$. There exists a Lagrangian fibration $f:X\rightarrow \mathbb{P}^r$ such that $L=f^*\mathcal{O}_{\mathbb{P}^r}(k)$ for some $k\geq 1$.
\mathrm{b)} There exists a hyperk\"ahler manifold $X'$ bimeromorphic to $X$ and a Lagrangian fibration $X'\righta... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 6
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,198 | AMR-118-0007 | Holomorphic Symplectic Geometry — Question 7 | Does every hyperk\"ahler manifold admit a deformation with a Lagrangian fibration? | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 7
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,199 | AMR-118-0008 | Holomorphic Symplectic Geometry — Question 8 | Let $X$ be a hyperk\"ahler manifold, and $T\subset X$ a Lagrangian submanifold which is a complex torus. Is it the fibre of a Lagrangian fibration $X\rightarrow \mathbb{P}^r$? | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 8
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,200 | AMR-118-0009 | Holomorphic Symplectic Geometry — Question 9 | Describe the general projective deformation of $S^{[2]}$, for $S$ a polarized K3 surface of genus $1$, $2$, $3$, ... (and for some choice of polarization on $S^{[2]}$); or at least find more examples of locally complete projective families. Same question with $S^{[r]}$ for $r\geq 3$. | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Question 9
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,201 | AMR-118-0010 | Holomorphic Symplectic Geometry — Conjecture 10 | Let $D_1,\ldots ,D_k$ in $\operatorname{Pic}(X)$, and let $z\in CH(X)$ be a class which is a polynomial in $D_1,\ldots ,D_k$ and the Chern classes $c_i(X)$. If $z=0$ in $H^*(X,\mathbb{Z})$, then $z=0$. | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 10
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,202 | AMR-118-0011 | Holomorphic Symplectic Geometry — Conjecture 11 | \[X=\sd_{s\ \mathrm{ even} }X_s \quad\hbox{where }\ X_s :=\{x\in X\ |\ \operatorname{rk} \tau (x)=s\}\ .
\]
The following conjecture is due to Bondal ([Bd], see also [P]):
If $X$ is Fano and $s$ even, $X_{\leq s}:=\sd_{k\leq s}X_k$ contains a component of dimension $>s$. | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 11
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,203 | AMR-118-0012 | Holomorphic Symplectic Geometry — Conjecture 12 | This is much larger than one would expect from a naive dimension count. It implies for instance that a Poisson field which vanishes at some point must vanish along a curve.
The condition ``$X$ Fano" is probably far too strong. In fact an optimistic modification would be :
If $X_s$ is non-empty, it contains a component... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 12
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,204 | AMR-118-0013 | Holomorphic Symplectic Geometry — Conjecture 13 | There are only two classes of compact holomorphic contact manifolds known so far:
a) The projective cotangent bundle $\mathbb{P} T^*_M$, where $M$ is any compact complex manifold;
b) Let $\mathfrak{g}$ be a simple complex Lie algebra. The action of the adjoint group on $\mathbb{P} (\mathfrak{g})$ has a unique closed or... | Source list: Beauville - Holomorphic Symplectic Geometry: A Problem List (2010)
Source item: Conjecture 13
Source URL: https://arxiv.org/abs/1002.4321
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Beauville | 2,010 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,205 | AMR-119-0001 | Several Complex Variables Problem List — Problem 1 | {\bf (New) (See Section 7.2.) Let $V$ be a germ at $0$ of an irreducible complex variety
in $\mathbb{C}^n.$ For any small enough $\epsilon > 0$, let
$E= E_\epsilon:= V \cap \mathbb{R}^n \cap \{|z|< \epsilon \}.$
Define the extremal function $U_E$ on $\{ |z|< \epsilon \}:
U_E(z):= \sup \{u(z); u \leq 0\; \mbox{on}\; E,\... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 1
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,206 | AMR-119-0002 | Several Complex Variables Problem List — Problem 2 | {\bf (New) (See Section 8.2.) What is the lowest degree of a polynomial mapping
$P: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ for which the (real) Jacobian conjecture
fails, i.e. the Jacobian of $P$ near vanishes while $p$ fails
to be invertible.} | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 2
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,207 | AMR-119-0003 | Several Complex Variables Problem List — Problem 3 | **(New) (See Section 11.3) (Liouville type assertion on CR 3-manifolds) On a CR 3-manifold
one can always define a Carnot-Caratheodory metric. A homeomorphism between
two strongly pseudoconvex CR 3-manifolds is called conformal if it maps
infinitesimal spheres with respect to a Carnot-Caratheodory metric to
infinitesim... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 3
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,208 | AMR-119-0004 | Several Complex Variables Problem List — Problem 4 | **(New) (See Section 11.3) A diffeomorphism between two strongly pseudoconvex CR
$(2n+1)$-manifolds is called quasiconformal if its differential preserves
the underlying contact structures and distorts the CR structures boundedly.
When Hermitian metrics on the contact bundles are fixed, this distortion
can be measured ... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 4
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,209 | AMR-119-0005 | Several Complex Variables Problem List — Problem 5 | Let M be a smooth real hypersurface in $\mathbb{C}^n$ with defining
function r. Let $p_0$ be a point in M, and let U be a neighborhood in $\mathbb{C}^n$
of $p_0$. When do C-R functions on $M\cap U$ extend to $\lbrace r > 0
\rbrace$?\\
-B. Stensones, berit@math.lsa.umich.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 5
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,210 | AMR-119-0006 | Several Complex Variables Problem List — Problem 6 | Let D be a bounded domain in $\mathbb{C}^n$ with smooth boundary, with
envelope of holomorphy $D^{\sim}$.
A)Is $D^{\sim}$ finitely sheeted over $\mathbb{C}^n$?
B) Does $D^{\sim}$ have finite volume?\\
-B. Stensones, berit@math.lsa.umich.edu. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 6
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,211 | AMR-119-0007 | Several Complex Variables Problem List — Problem 7 | If D is a strictly pseudoconvex domain in $\mathbb{C}^2$ diffeomorphic to $\mathbb{R}^4$ and A is an embedded
analytic disc outside D with $bA \subset bD$, then there is an embedded smooth disc
M in D, with bM=bA, and such that M is totally real except at
one elliptic point. With such a configuration
(M,A) in $\mathbb{... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 7
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,212 | AMR-119-0008 | Several Complex Variables Problem List — Problem 8 | Let $U$ be an open subset of a Stein space. If $U$ is locally Stein,
is $U$ Stein?\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 8
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,213 | AMR-119-0009 | Several Complex Variables Problem List — Problem 9 | Let M be a compact complex manifold. Find some appropriate
conditions on M such that if U is an open subset of M which is
locally Stein, then U is Stein.\\
-N. Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 9
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,214 | AMR-119-0010 | Several Complex Variables Problem List — Problem 10 | Let $X$ be a complex subvariety of the unit ball $\mathbb{B}$ with an isolated
singularity at the origin. Suppose $\Omega_t$ is a continuously increasing
family of Stein open subsets of $X$. Also, suppose that $0 \in \partial \Omega_{1/2} ,
0\in \Omega_t, t>1/2.$ Is $\Omega_s$ Runge in $\Omega_t$ $\forall s<t$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 10
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,215 | AMR-119-0011 | Several Complex Variables Problem List — Problem 11 | Let $K^{compact} \subset X \backslash \lbrace 0 \rbrace$, $X$ as above,
$0 \in \hat{K}$, the polynomially convex hull of $K$. Suppose that $L \subset X$,
$L$ contains a neighborhood of $K$ in $X$. Does $\hat{L}$ contain a neighborhood
of $0$ in $X$? (This is equivalent to the previous problem.)\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 11
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,216 | AMR-119-0012 | Several Complex Variables Problem List — Problem 12 | Let $\lbrace U_n \rbrace$ be an increasing sequence of Stein open subsets of
a Stein Space $X$. Is $\bigcup_{n=1}^{\infty} U_n$ Stein? (If X is a complex
manifold, not necessarily Stein, the answer is in general no.)\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 12
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,217 | AMR-119-0013 | Several Complex Variables Problem List — Problem 13 | Suppose $M$ is a complex manifold of dimension 2, and suppose $\forall K^{compact}
\subset M$ there exists an open subset $U$, $K \subset U \subset M$ such that
$U$ is biholomorphic to the unit ball. Does this imply that M is equivalent to
the unit ball $\mathbb{B}$, $\Delta \times \mathbb{C}$ or $\mathbb{C}^2$? (This ... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 13
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,218 | AMR-119-0014 | Several Complex Variables Problem List — Problem 14 | Is ``long'' $\mathbb{C}^2$ biholomorphic to $\mathbb{C}^2$? ( A complex manifold is a long
$\mathbb{C}^2$ if it is the union of proper subsets that are biholomorphic to $\mathbb{C}^2$.)\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 14
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,219 | AMR-119-0015 | Several Complex Variables Problem List — Problem 15 | Let $\Omega \subset \subset \mathbb{C}^n$ be a smooth pseudoconvex
domain. Let $A^k(\bar\Omega)= H(\Omega)\cap C^k(\bar\Omega)$
with $C^k$ topology, $1 \leq k \leq \infty$. Is $A^{\infty}(\bar\Omega)$
dense in $A^k(\bar\Omega)$?\\
-N. Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 15
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,220 | AMR-119-0016 | Several Complex Variables Problem List — Problem 16 | Let $\Omega \subset \subset \mathbb{C}^n$ be a smooth pseudoconvex
domain. Assume that $\bar\Omega$ has a Stein neighborhood basis. Is
every function in $A^{\infty}(\bar\Omega)$ uniformly approximable
by holomorphic functions in a neighborhood of $\bar\Omega$?\\
-N. Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 16
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,221 | AMR-119-0017 | Several Complex Variables Problem List — Problem 17 | Let $f_1, ..., f_k$ be bounded holomorphic functions on $\Omega.$
Suppose $\sum |f_i|> c> 0.$ The Corona problem is whether there exist
bounded holomorphic funcions $g_1, ..., g_k$ on $\Omega$ such
that $\sum f_i g_i \equiv 1.$ Can the Corona problem be solved if $\Omega$
is the unit ball or the unit polydisc? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 17
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,222 | AMR-119-0018 | Several Complex Variables Problem List — Problem 18 | \ \ \
Let $\Phi =\{ \Phi^0, \Phi^1, \Phi^2, \Phi^3\}$ be a subset of the body
$(=skew-field) \ \mathbb{H}$ of the real quaternions with the conditions
$$
\Phi^p \bar\Phi^q + \Phi^q \bar\Phi^p = 2 \delta_{p,q},
$$
$\Omega$ is a domain in $\mathbb{R}^4=\mathbb{C}^2$. On the $\mathbb{H}$-bimodule $C^1(\Omega ;
\mathbb{H})... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 18
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,223 | AMR-119-0019 | Several Complex Variables Problem List — Problem 19 | Is every boundary point of a bounded pseudoconvex domain $D$ in $\mathbb{C}^n$ of
finite type a peak point for $A(D)$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 19
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,224 | AMR-119-0020 | Several Complex Variables Problem List — Problem 20 | Describe peak sets on weakly pseudoconvex domains of finite type. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 20
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,225 | AMR-119-0021 | Several Complex Variables Problem List — Problem 21 | Characterize the representing measures for the origin in
the unit ball in $\mathbb{C}^n.$ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 21
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,226 | AMR-119-0022 | Several Complex Variables Problem List — Problem 22 | Let $X \subset \mathbb{C}^n$ be compact
and totally disconnected. Assume that $X$ has finite one-dimensional Hausdorff
measure. Then is $X$ polynomially convex?\\
-H. Alexander, U22330@UICVM.bitnet | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 22
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,227 | AMR-119-0023 | Several Complex Variables Problem List — Problem 23 | Let $\Omega \subset \mathbb{C}^n$ be a smoothly bounded, pseudoconvex domain.
Let $V \subseteq \Omega$ be a divisor which is bounded away from the
Silov boundary in $\partial \Omega.$ Prove that there is a bounded
holomorphic function on $\Omega$ that vanishes on $V.$ (This is known
for the polydisc---a result of Rudin... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 23
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,228 | AMR-119-0024 | Several Complex Variables Problem List — Problem 24 | Give a geometric characterization of zero sets of $H^p$ functions on
strongly pseudoconvex domains. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 24
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,229 | AMR-119-0025 | Several Complex Variables Problem List — Problem 26 | Solve $\bar\partial \; Neumann$ in $L^2 (d\mu)$, $d\mu$ a measure, even on the
unit disc. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 26
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,230 | AMR-119-0026 | Several Complex Variables Problem List — Problem 27 | Let $\Omega$ be a smooth bounded planar domain and let $T:L^2(\Omega)\mapsto
L^2(\Omega)$ be the Kohn solution operator for $\partial/\partial\bar z$. For
$h\in L^\infty(\Omega)$ we define the compact non-self-adjoint operator
$S_h:L^2(\Omega)\mapsto L^2(\Omega), f\mapsto \bar hTf$. Under what circumstance
will $S_h$ h... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 27
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,231 | AMR-119-0027 | Several Complex Variables Problem List — Problem 28 | If D is a real analytically bounded pseudoconvex domain in $\mathbb{C}^n$,
is the $\bar\partial$ Neumann problem globally real analytic hypoelliptic
up to the boundary?\\
- D. S. Tartakoff, U22393@UICVM.bitnet | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 28
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,232 | AMR-119-0028 | Several Complex Variables Problem List — Problem 29 | If M is a compact real analytic pseudoconvex CR manifold
of real dimension at least 5 is $\Box_b$ globally real
analytic hypoelliptic (say on (0,1) forms) on M?\\
- D. S. Tartakoff, U22393@UICVM.bitnet | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 29
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,233 | AMR-119-0029 | Several Complex Variables Problem List — Problem 30 | Can one solve $\bar\partial$ with H\"{o}lder estimates on any real
analytic bounded pseudoconvex domain in $\mathbb{C}^n$?\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 30
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,234 | AMR-119-0030 | Several Complex Variables Problem List — Problem 31 | Solve $\bar\partial$ in $L^p$ in bounded pseudoconvex domains, without necessarily
smooth boundary, $1 < p < 2$. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 31
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,235 | AMR-119-0031 | Several Complex Variables Problem List — Problem 32 | Solve $\bar\partial$ with $L^p$ estimates, $1< p< \infty$ for smooth convex
domains in $\mathbb{C}^n$. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 32
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,236 | AMR-119-0032 | Several Complex Variables Problem List — Problem 33 | Can one solve $\bar \partial u = f$ in sup norm on smooth bounded convex
domains in $\mathbb{C}^2$?\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 33
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,237 | AMR-119-0033 | Several Complex Variables Problem List — Problem 34 | Which geometric properties of the domain do uniform estimates depend on?
$\lbrack e.g. L^2$ estimates depend on the diameter and the dimension
$\rbrack$. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 34
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,238 | AMR-119-0034 | Several Complex Variables Problem List — Problem 35 | If $\Omega \subset \subset \mathbb{C}^n$ is pseudoconvex with smooth boundary, does
$\bar \partial: \Lambda^{\alpha}(\bar \Omega) \mapsto \Lambda_{(0, 1)}^{\beta}
(\bar \Omega)$ have closed range if $\alpha < \beta$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 35
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,239 | AMR-119-0035 | Several Complex Variables Problem List — Problem 36 | Let $\Omega$ in $\mathbb{C}^n$ be a bounded biholomorphic image of the unit ball
in $\mathbb{C}^n$. Does the $\bar\partial$ satisfy uniform estimates on $\Omega$?
The problem is of interest mainly when $\Omega$ has very rough boundary.\\
-B. Berndtsson, bob@math.chalmers.se | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 36
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,240 | AMR-119-0036 | Several Complex Variables Problem List — Problem 37 | Does there exist a pseudoconvex domain in $\mathbb{C}^2 $ with the same homotopy
type as $S^2$?\\
-F. Forstneric, forstner@math.wisc.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 37
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,241 | AMR-119-0037 | Several Complex Variables Problem List — Problem 38 | Is B complete on bounded pseudoconvex domains with less than $C^1$
boundary?\\
-J. McNeal, mcneal@math.princeton.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 38
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,242 | AMR-119-0038 | Several Complex Variables Problem List — Problem 39 | For which domains is the Bergman kernal function $K(z, w)$ nonvanishing
everywhere? This is related to Lu Qi-Keng conjecture. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 39
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,243 | AMR-119-0039 | Several Complex Variables Problem List — Problem 41 | Is there a smoothly bounded pseudoconvex domain in $\mathbb{C}^n$ on which the
Kobayashi and Caratheodory metrics are not comparable?
-S. Krantz, SK@math.wustl.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 41
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,244 | AMR-119-0040 | Several Complex Variables Problem List — Problem 42 | Is the regular order of contact of a smooth pseudoconvex domain the same as
the commutator type, one vector field at a time.\\
-J. McNeal, mcneal@math.princeton.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 42
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,245 | AMR-119-0041 | Several Complex Variables Problem List — Problem 43 | Are finite type pseudoconvex domains in $\mathbb{C}^2$ locally convexifiable
with biholomorphic
maps with continuous boundary values? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 43
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,246 | AMR-119-0042 | Several Complex Variables Problem List — Problem 45 | What's the asymptotic behavior of k on finite type domains in $\mathbb{C}^n$? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 45
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,247 | AMR-119-0043 | Several Complex Variables Problem List — Problem 46 | Let $D = \lbrace z \in \mathbb{C}^n ; h(z) < 1 \rbrace$ be a bounded pseudoconvex
complete$-$circular domain with
Minkowski function h. Characterize the Caratheodory, the Bergman or the
Kobayashi completeness of D via properties of h.
[The following is known: a) If h is continuous, then D is Bergman
complete. b) If $n\... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 46
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,248 | AMR-119-0044 | Several Complex Variables Problem List — Problem 47 | Given a compact complex hypersurface X in $\mathbb{P}^n$ with degree at least $n+2$ and
only normal crossing singularities. Show that the infinitesimal Kobayashi
pseudometric
on $\mathbb{P}^n \setminus X$ is degenerate at most on a complex hypersurface.\\
-N. Sibony, sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 47
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,249 | AMR-119-0045 | Several Complex Variables Problem List — Problem 48 | Find (or prove it does not exist) a complete hyperbolic manifold not
biholomorphic to a
convex domain where the Kobayashi and Carath\'eodory distances agree
everywhere.\\
-M. Abate, abate@vaxsns.infn.it | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 48
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,250 | AMR-119-0046 | Several Complex Variables Problem List — Problem 49 | Can you recover certain
derivatives of the Levi form at a weakly pseudoconvex point in terms
of the weighted boundary behavior of the Kobayashi metric?\\
-S. Krantz, sk@math.wustl.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 49
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,251 | AMR-119-0047 | Several Complex Variables Problem List — Problem 50 | Let $\Omega \subset \subset \mathbb{C}^n$ be pseudoconvex with smooth boundary.
For $K \subset \bar\Omega$ compact, let $\hat K:= \lbrace z \in \bar \Omega ;
\phi(z) \leq sup_K \phi, \phi$ continuous on $\bar \Omega, \phi$
plurisubharmonic on $\Omega \rbrace$. Assume $\hat K \cap \partial \Omega = K
\cap \partial \Omeg... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 50
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,252 | AMR-119-0048 | Several Complex Variables Problem List — Problem 51 | Find conditions insuring that if a sequence of plurisubharmonic functions
$u_m \rightarrow u$ in $\mathbb{C}^n$ then $(dd^c u_m)^n \rightarrow (dd^c u)^n$. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 51
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,253 | AMR-119-0049 | Several Complex Variables Problem List — Problem 52 | {\bf (New) Let $V$ be a germ at $0$ of an irreducible complex variety
in $\mathbb{C}^n.$ For any small enough $\epsilon > 0$, let
$E= E_\epsilon:= V \cap \mathbb{R}^n \cap \{|z|< \epsilon \}.$
Define the extremal function $U_E$ on $\{ |z|< \epsilon \}:
U_E(z):= \sup \{u(z); u \leq 0\; \mbox{on}\; E,\;
0 \leq u \leq 1 \... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 52
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,254 | AMR-119-0050 | Several Complex Variables Problem List — Problem 53 | Which smooth domains have non compact automorphism groups?\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 53
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,255 | AMR-119-0051 | Several Complex Variables Problem List — Problem 54 | If P: $\mathbb{C}^2 \rightarrow \mathbb{C}^2$ is a holomorphic polynomial map with nonvanishing
Jacobian, then P is biholomorphic. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 54
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,256 | AMR-119-0052 | Several Complex Variables Problem List — Problem 55 | {\bf (New) What is the lowest degree of a polynomial mapping
$P: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ for which the (real) Jacobian conjecture
fails, i.e. the Jacobian of $P$ never vanishes while $p$ fails
to be invertible.} | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 55
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,257 | AMR-119-0053 | Several Complex Variables Problem List — Problem 56 | Classify Proper Holomorphic Correspondences from the unit disc to itself. | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 56
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,258 | AMR-119-0054 | Several Complex Variables Problem List — Problem 57 | Is every proper holomorphic self-mapping
of a smooth bounded domain in $\mathbb{C}^n (n>1)$ biholomorphic? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 57
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,259 | AMR-119-0055 | Several Complex Variables Problem List — Problem 58 | Does f have a continuous extension to $\bar U$? (This is true if U, V are
pseudoconvex.) | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 58
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,260 | AMR-119-0056 | Several Complex Variables Problem List — Problem 59 | If M is an n-dimensional parallellizable Stein manifold, can M
be holomorphically immersed in $\mathbb{C}^n$?
[ True for n=1 (Gunning and Narasimhan); also such an M can be immersed in
$\mathbb{C}^{n+1}$ (Eliashberg-Gromov)].
\\
-R. Narasimhan, Dept. of Math., Univ. of Chicago, Chicago, IL 60637 | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 59
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,261 | AMR-119-0057 | Several Complex Variables Problem List — Problem 60 | Can $SL(n, \mathbb{C})$ be holomorphically immersed in $\mathbb{C}^{n^2-1}$.
[Cannot be done algebraically, true if n=2]\\
-R. Narasimhan, Dept. of Math., Univ. of Chicago, Chicago, IL 60637 | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 60
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,262 | AMR-119-0058 | Several Complex Variables Problem List — Problem 61 | Can the algebraic hypersurface
$$ w^3 + w g(w_1, ......, w_n) + f(w_1, ......, w_n) = 1, $$
where g is homogeneous of degree 2 and f homogeneous of degree 3, be
holomorphically immersed in $\mathbb{C}^n$
[ Not true for algebraic immersion]\\
-R. Narasimhan, Dept. of Math., Univ. of Chicago, Chicago, IL 60637 | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 61
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,263 | AMR-119-0059 | Several Complex Variables Problem List — Problem 62 | Suppose that the polynomial equation
$$F(w_0, w_1, ......, w_n)=1$$
defines a smooth
affine algebraic hypersurface (these are always parallellizable
(Murthy, Swan, n=2; Suslin for general n). Can they be holomorphically
immersed in
$\mathbb{C}^n$?\\
-R. Narasimhan, Dept. of Math., Univ. of Chicago, Chicago, IL 60637 | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 62
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,264 | AMR-119-0060 | Several Complex Variables Problem List — Problem 63 | Do there exist Fatou--Bieberbach domains which are not Runge?
A Fatou--Bieberbach domain is a proper subdomain of $\mathbb{C}^2$ which is
biholomorphic to $\mathbb{C}^2$.\\
-F. Forstneric, forstner@math.wisc.edu | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 63
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,265 | AMR-119-0061 | Several Complex Variables Problem List — Problem 64 | Do there exist wandering domains for complex Henon maps? | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 64
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,266 | AMR-119-0062 | Several Complex Variables Problem List — Problem 65 | The Fatou Set of a Polynomial Automorphism of $\mathbb{C}^2$.
Let $f$ be a polynomial automorphism of $\mathbb{C}^2$, and suppose that $f$ is
not conjugate to an elementary map. Let $\Omega$ be a connected component of
the set of points where the forward iterates $\lbrace f^n:n=1,2,3,...\rbrace $
are locally bounded, w... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 65
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,267 | AMR-119-0063 | Several Complex Variables Problem List — Problem 66 | Let $ F_c : (z,w) \rightarrow (z^2 +c - w, z)$, $c \in \mathbb{C}$ a symplectic
automorphism of $\mathbb{C}^2$, i.e. $F_c$ is biholomorphic and $ F^*_c(dz \wedge dw) = dz \wedge dw$. Can there exist a $c \in \mathbb{C}$ and a periodic orbit $\{z_i\}^k_{i=0}$ for $F_c$ such that $z_0$ belongs to a Siegel domain ?\\
-M. ... | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 66
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,268 | AMR-119-0064 | Several Complex Variables Problem List — Problem 67 | Suppose $f$ is a holomorphic map on $\mathbb{P}^2$ of degree $d \geq 2$.
Must $f$ have a repelling fixed point.\\ | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 67
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,269 | AMR-119-0065 | Several Complex Variables Problem List — Problem 68 | Does every holomorphic map $F:\mathbb{P}^k \rightarrow \mathbb{P}^k$ of degree at least two have a repelling periodic point? Do meromorphic maps have periodic orbits?
-sibony@anh.matups.fr | Source list: Buzzard, Fornaess, Krantz - The Several Complex Variables Problem List (1995)
Source item: Problem 68
Source URL: https://arxiv.org/abs/math/9509202
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Buzzard, Fornaess, Krantz | 1,995 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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