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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...
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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...
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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...
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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...
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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...
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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...
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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
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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
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Hamieh, Kadiri, Ng
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2026-10-16T14:00:00
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{ "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...
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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
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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
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null
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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
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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
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null
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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
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null
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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
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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
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null
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null
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null
null
null
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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
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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
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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...
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null
null
null
null
null
null
null
null
null
null
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null
null
null
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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
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null
null
null
null
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null
null
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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...
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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...
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null
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null
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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...
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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...
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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
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null
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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
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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
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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
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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
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null
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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
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null
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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...
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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...
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null
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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
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null
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null
null
null
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null
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null
null
null
null
null
null
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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
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null
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null
null
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null
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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
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null
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null
null
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null
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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
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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...
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null
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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
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null
null
null
null
null
null
null
null
null
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null
null
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null
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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...
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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...
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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...
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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...
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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...
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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
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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...
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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...
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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
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null
null
null
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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...
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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...
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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...
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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...
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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...
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null
null
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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...
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null
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null
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null
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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...
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null
null
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null
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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
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null
null
null
null
null
null
null
null
null
null
null
null
null
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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
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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
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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
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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
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null
null
null
null
null
null
null
null
null
null
null
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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
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null
null
null
null
null
null
null
null
null
null
null
null
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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
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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
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null
null
null
null
null
null
null
null
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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
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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