Number Theory

Authors and titles for June 2024

[201] arXiv:2406.20013 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Heights on 'Hybrid orbits' in Shimura varieties Show Chinese title

Title: Shimura流形上的'混合轨道'高度

Rodolphe Richard, Andrei Yafaev

Subjects: Number Theory (math.NT)

[202] arXiv:2406.00139 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity Show Chinese title

Title: 组合证明涉及按奇偶性分离部分的分拆数的不等式

Cristina Ballantine, Amanda Welch

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[203] arXiv:2406.00381 (cross-list from math.AC) [cn-pdf, pdf, html, other]

Title: On Fuchs' problem for finitely generated abelian groups: The small torsion case Show Chinese title

Title: 关于有限生成阿贝尔群的Fuchs问题：小扭子情况

I. Del Corso, L. Stefanello

Subjects: Commutative Algebra (math.AC) ; Group Theory (math.GR) ; Number Theory (math.NT)

[204] arXiv:2406.00463 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Certaines fibrations en surfaces quadriques réelles Show Chinese title

Title: 某些实二次曲面纤维化

Jean-Louis Colliot-Thélène, Alena Pirutka

Comments: 44 pages, in French language

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[205] arXiv:2406.00835 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Algebroid maps and hyperbolicity of symmetric powers Show Chinese title

Title: 代数映射与对称幂的双曲性

Natalia Garcia-Fritz, Hector Pasten

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[206] arXiv:2406.01828 (cross-list from math-ph) [cn-pdf, pdf, html, other]

Title: Spectral Flow for the Riemann zeros Show Chinese title

Title: 谱流对于黎曼零点

André LeClair

Comments: 18 page. Version 2: fixed some typesetting errors. Also added an argument that the free part of the underlying hamiltonian is hermitian with an energy gap. Version 3: Published version in Advances in Theoretical and Mathematical Physics 2025; includes a study of random matrix statistics off of the critical line

Journal-ref: Advances in Theoretical and Mathematical Physics 2025

Subjects: Mathematical Physics (math-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn) ; High Energy Physics - Theory (hep-th) ; Number Theory (math.NT)

[207] arXiv:2406.02182 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Berthelot's conjecture via homotopy theory Show Chinese title

Title: 通过同伦理论的伯特洛特猜想

Veronika Ertl, Alberto Vezzani

Comments: 34 pages. The comparison to Berthelot's rigid cohomology has been expanded. To appear in Duke

Subjects: Algebraic Geometry (math.AG) ; K-Theory and Homology (math.KT) ; Number Theory (math.NT)

[208] arXiv:2406.02244 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On the characterization of chordal graphs using Horn hypergeometric series Show Chinese title

Title: 关于使用Horn超几何级数表征弦图的研究

Dipnit Biswas, Irfan Habib, R. Venkatesh

Comments: 15 pages, typos were fixed

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[209] arXiv:2406.02259 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Restricted SDC Edge Cover Pebbling Number Show Chinese title

Title: 限制SDC边覆盖钉数

A. Lourdusamy, F. Joy Beaula, F. Patrick, I. Dhivviyanandam

Comments: 9

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[210] arXiv:2406.02403 (cross-list from math.HO) [cn-pdf, pdf, html, other]

Title: Riemann's auxiliary Function. Basic Results Show Chinese title

Title: 黎曼的辅助函数 基本结果

J. Arias de Reyna

Comments: 12 pages, 2 figures

Subjects: History and Overview (math.HO) ; Number Theory (math.NT)

[211] arXiv:2406.03275 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Improved stability for the size and structure of sumsets Show Chinese title

Title: 改进和的大小与结构的稳定性

Andrew Granville, Jack Smith, Aled Walker

Comments: 15 pages

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[212] arXiv:2406.03453 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On a sign-change conjecture of Schlosser and Zhou Show Chinese title

Title: 关于Schlosser和Zhou的一个变号猜想

Kathrin Bringmann, Bernhard Heim, Ben Kane

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[213] arXiv:2406.03495 (cross-list from cs.LG) [cn-pdf, pdf, html, other]

Title: Grokking Modular Polynomials Show Chinese title

Title: 理解模多项式

Darshil Doshi, Tianyu He, Aritra Das, Andrey Gromov

Comments: 7+4 pages, 3 figures, 2 tables

Subjects: Machine Learning (cs.LG) ; Disordered Systems and Neural Networks (cond-mat.dis-nn) ; High Energy Physics - Theory (hep-th) ; Number Theory (math.NT) ; Machine Learning (stat.ML)

[214] arXiv:2406.03830 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: Single radius spherical cap discrepancy on compact two-point homogeneous spaces Show Chinese title

Title: 紧致两点齐次空间上的单半径球冠偏差

Luca Brandolini, Bianca Gariboldi, Giacomo Gigante, Alessandro Monguzzi

Comments: 16 pages

Subjects: Classical Analysis and ODEs (math.CA) ; Number Theory (math.NT)

[215] arXiv:2406.03891 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Vanishing criteria for Ceresa cycles Show Chinese title

Title: 消失准则 for Ceresa 循环

Jef Laga, Ari Shnidman

Comments: 24 pages, added more examples, comments welcome

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[216] arXiv:2406.04034 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: The geometry of intersecting codes and applications to additive combinatorics and factorization theory Show Chinese title

Title: 相交码的几何及其在加法组合学和分解理论中的应用

Martino Borello, Wolfgang Schmid, Martin Scotti

Comments: 31 pages

Subjects: Combinatorics (math.CO) ; Information Theory (cs.IT) ; Number Theory (math.NT)

[217] arXiv:2406.04045 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On the Diameter of Undirected Cayley Graphs of Finite Abelian Groups Show Chinese title

Title: 关于有限阿贝尔群的无向Cayley图的直径

Bela Bajnok, W. Kyle Beatty

Journal-ref: Comb. Number Th. 14 (2025) 1-12

Subjects: Combinatorics (math.CO) ; Group Theory (math.GR) ; Number Theory (math.NT)

[218] arXiv:2406.04718 (cross-list from cs.CR) [cn-pdf, pdf, html, other]

Title: From Worst to Average Case to Incremental Search Bounds of the Strong Lucas Test Show Chinese title

Title: 从最坏情况到平均情况再到增量搜索的强卢卡斯测试边界

Semira Einsele, Gerhard Wunder

Comments: To be published in the proceedings (LNCS Springer) of the conference Number-Theoretic Methods in Cryptology 2024

Subjects: Cryptography and Security (cs.CR) ; Number Theory (math.NT)

[219] arXiv:2406.05099 (cross-list from math.QA) [cn-pdf, pdf, other]

Title: Canonicalizing zeta generators: genus zero and genus one Show Chinese title

Title: 规范ζ生成元：零亏格和一亏格

Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Oliver Schlotterer, Leila Schneps, Bram Verbeek

Comments: 92 pages. Submission includes ancillary data files. v2: Typos corrected

Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Phenomenology (hep-ph) ; High Energy Physics - Theory (hep-th) ; Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[220] arXiv:2406.05523 (cross-list from math.PR) [cn-pdf, pdf, other]

Title: Stochastic Calculus for the Theta Process Show Chinese title

Title: 用于Theta过程的随机微积分

Francesco Cellarosi, Zachary Selk

Comments: 61 pages. Applications of rough paths theory to number theory

Subjects: Probability (math.PR) ; Dynamical Systems (math.DS) ; Group Theory (math.GR) ; Number Theory (math.NT) ; Representation Theory (math.RT)

[221] arXiv:2406.06206 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: A lower bound for the number of pinned angles determined by a Cartesian product set Show Chinese title

Title: 由笛卡尔乘积集确定的固定角的数量的下界

Oliver Roche-Newton

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[222] arXiv:2406.06439 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Topological Applications of p-Adic Divergence and Gradient Operators Show Chinese title

Title: p进散度和梯度算子的拓扑应用

Patrick Erik Bradley

Comments: 22 pages. Typos. Some statements corrected. Introduction expanded. Bibliographical reference added

Subjects: Analysis of PDEs (math.AP) ; Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[223] arXiv:2406.06945 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Probabilistic degenerate Stirling numbers of the first kind and their applications Show Chinese title

Title: 概率退化第一类斯特林数及其应用

Taekyun Kim, Dae san Kim

Comments: 15 pages

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT) ; Probability (math.PR)

[224] arXiv:2406.06956 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture Show Chinese title

Title: 对数平均的Sarnak猜想中的任意缓慢衰减

Amir Algom, Zhiren Wang

Comments: Preprint version, 12 pages. To appear in JMAA

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[225] arXiv:2406.07223 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Rational points on even dimensional Fermat cubics Show Chinese title

Title: 高维费马三次曲线上的有理点

Alex Massarenti

Comments: 26 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT) ; Rings and Algebras (math.RA)

[226] arXiv:2406.07401 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Exceptional Tannaka groups only arise from cubic threefolds Show Chinese title

Title: 例外的Tannaka群仅来自三次三维流形

Thomas Krämer, Christian Lehn, Marco Maculan

Subjects: Algebraic Geometry (math.AG) ; Complex Variables (math.CV) ; Number Theory (math.NT)

[227] arXiv:2406.07639 (cross-list from math.CV) [cn-pdf, pdf, html, other]

Title: Estimates of automorphic forms on $\mathrm{SU}(n,1)$ Show Chinese title

Title: $\mathrm{SU}(n,1)$上的自守形式估计

Anilatmaja Aryasomayajula, Baskar Balasubramanyam

Comments: This is the first draft, and any comments, suggestions, and remarks are most welcome. arXiv admin note: text overlap with arXiv:2301.11160

Subjects: Complex Variables (math.CV) ; Number Theory (math.NT)

[228] arXiv:2406.08017 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: The defect of weak approximation for a reductive group over a global field Show Chinese title

Title: 一个整体域上约化群的弱逼近缺陷

Mikhail Borovoi, Jean-Louis Colliot-Thélène

Comments: v7: 27 pages, including the listing of a Magma program; v8: 29 pages, including an appendix by J.-L. Colliot-Th\'el\`ene

Subjects: Representation Theory (math.RT) ; Algebraic Geometry (math.AG) ; Group Theory (math.GR) ; Number Theory (math.NT)

[229] arXiv:2406.08692 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: The cancellation property for projective modules over integral group rings Show Chinese title

Title: 投影模在整数群环上的消去性质

John Nicholson

Comments: 39 pages. Minor update to account for an inaccuracy in the article of Bley-Hofmann-Johnston (arXiv:2407.02294) which has now been fixed. The group I x C2 = SmallGroup(240, 94) fails SFC, but was previously stated as having SFC. The statement of Theorem A has been adjusted accordingly

Subjects: Group Theory (math.GR) ; Algebraic Topology (math.AT) ; K-Theory and Homology (math.KT) ; Number Theory (math.NT)

[230] arXiv:2406.09059 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Distribution of hooks in self-conjugate partitions Show Chinese title

Title: 自共轭分拆中的钩子分布

William Craig, Ken Ono, Ajit Singh

Comments: Corrected one formula based on referee's comment

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[231] arXiv:2406.09150 (cross-list from cs.DS) [cn-pdf, pdf, html, other]

Title: Reducing the Space Used by the Sieve of Eratosthenes When Factoring Show Chinese title

Title: 减少分解因数时筛法使用的空间

Samuel Hartman, Jonathan P. Sorenson

Subjects: Data Structures and Algorithms (cs.DS) ; Number Theory (math.NT)

[232] arXiv:2406.09210 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Davenport constant and its variants for some non-abelian groups Show Chinese title

Title: 达文波特常数及其在某些非阿贝尔群中的变体

C. G. Karthick Babu, Ranjan Bera, Mainak Ghosh, B. Sury

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[233] arXiv:2406.09283 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Local Langlands in families: The banal case Show Chinese title

Title: 局部朗兰兹族：平凡情形

Jean-François Dat, David Helm, Robert Kurinczuk, Gilbert Moss

Comments: 57 pages

Subjects: Representation Theory (math.RT) ; Number Theory (math.NT)

[234] arXiv:2406.09361 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On the independence number of sparser random Cayley graphs Show Chinese title

Title: 关于更稀疏的随机Cayley图的独立数

Marcelo Campos, Gabriel Dahia, João Pedro Marciano

Comments: Small adjustments following a helpful referee report, version accepted for publication in the Journal of the London Mathematical Society

Journal-ref: J. Lond. Math. Soc. 110 (2024)

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[235] arXiv:2406.09632 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Non-$μ$-ordinary smooth cyclic covers of $\mathbb{P}^1$ Show Chinese title

Title: 非$μ$-平凡光滑循环覆盖的$\mathbb{P}^1$

Yuxin Lin, Elena Mantovan, Deepesh Singhal

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[236] arXiv:2406.09848 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: On Isolated Gaps of Numerical Semigroups of embedding dimension two Show Chinese title

Title: 关于嵌入维数为二的数值半群的孤立间隙

Shubh N. Singh, Ranjan K. Ram

Comments: 8 pages

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[237] arXiv:2406.10145 (cross-list from math.NA) [cn-pdf, pdf, html, other]

Title: Reconstruction Plans and Efficient Rank-1 Lattice Construction for Chebyshev Expansions Over Lower Sets Show Chinese title

Title: 重构计划和用于下集上切比雪夫展开的高效秩-1格构构造

Abdelqoddous Moussa, Moulay Abdellah Chkifa

Subjects: Numerical Analysis (math.NA) ; Number Theory (math.NT)

[238] arXiv:2406.10800 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Injectivity theorems and cubical descent for schemes, stacks, and analytic spaces Show Chinese title

Title: 可注入性定理和立方下降对于概形、堆栈和解析空间

Takumi Murayama

Comments: Comments welcome. v1: 65 pages

Subjects: Algebraic Geometry (math.AG) ; Complex Variables (math.CV) ; Number Theory (math.NT)

[239] arXiv:2406.10872 (cross-list from cs.IT) [cn-pdf, pdf, html, other]

Title: On entropy Marton-type inequalities and small symmetric differences with cosets of abelian groups Show Chinese title

Title: 关于熵马尔顿型不等式与阿贝尔群陪集的小对称差

Thomas Karam

Comments: 10 pages, submitted

Subjects: Information Theory (cs.IT) ; Combinatorics (math.CO) ; Group Theory (math.GR) ; Number Theory (math.NT) ; Probability (math.PR)

[240] arXiv:2406.10919 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: A new family of expansions of real numbers Show Chinese title

Title: 实数的新一族展开式

Jörg Neunhäuserer

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[241] arXiv:2406.11510 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Rigidity of periodic points for loxodromic automorphisms of affine surfaces Show Chinese title

Title: 双曲自同构的仿射曲面上周期点的刚性

Marc Abboud (UNINE)

Comments: The initial version of this paper has been split into two papers. This new version is one of them

Subjects: Algebraic Geometry (math.AG) ; Complex Variables (math.CV) ; Dynamical Systems (math.DS) ; Number Theory (math.NT)

[242] arXiv:2406.12049 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts Show Chinese title

Title: 分拆和不包含重复奇数部分的分拆的刻度的组合解释

Frank G. Garvan, Rishabh Sarma

Journal-ref: SIGMA 20 (2024), 097, 14 pages

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[243] arXiv:2406.12734 (cross-list from math.AT) [cn-pdf, pdf, html, other]

Title: Unstable cohomology of $\mathsf{GL}_{2n}(\mathbb{Z})$ and the odd commutative graph complex Show Chinese title

Title: 不稳定上同调的$\mathsf{GL}_{2n}(\mathbb{Z})$以及奇数交换图复形

Francis Brown, Simone Hu, Erik Panzer

Comments: 77 pages, ancillary files with Pfaffian forms and integrals of graphs

Subjects: Algebraic Topology (math.AT) ; Geometric Topology (math.GT) ; Number Theory (math.NT) ; Quantum Algebra (math.QA)

[244] arXiv:2406.12766 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: On a p-adic version of Narasimhan and Seshadri's theorem Show Chinese title

Title: 关于p进制Narasimhan和Seshadri定理的一个版本

Fabrizio Andreatta

Comments: Using the paper "Higgs bundles over the good reduction of a quaternionic Shimura curve" by Mao Sheng, Jiajin Zhang, Kang Zuo, one can constrct a counterexample to the main claim of the paper

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[245] arXiv:2406.12791 (cross-list from math.CV) [cn-pdf, pdf, html, other]

Title: Hilbert's tenth problem for rings of holomorphic functions of bounded order Show Chinese title

Title: 希尔伯特第十问题对于有界阶的全纯函数环

Hector Pasten

Subjects: Complex Variables (math.CV) ; Logic (math.LO) ; Number Theory (math.NT)

[246] arXiv:2406.13077 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: An extension of Gauss's arithmetic-geometric mean (AGM) to three variables iteration scheme Show Chinese title

Title: 高斯算术-几何平均值（AGM）到三个变量迭代方案的扩展

Kiyoshi Sogo

Comments: 10 pages, 0 figures

Subjects: Classical Analysis and ODEs (math.CA) ; Number Theory (math.NT)

[247] arXiv:2406.13241 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's L-series Show Chinese title

Title: 三维流形Sol的非手性，Stevenhagen猜想和Shimizu的L级数

Ye Tian, Shicheng Wang, Zhongzi Wang

Comments: 19 pages

Subjects: Geometric Topology (math.GT) ; Number Theory (math.NT)

[248] arXiv:2406.13432 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Ramanujan vector field Show Chinese title

Title: 拉马努金向量场

Hossein Movasati

Comments: The article is now is a section of a new article "Leaf scheme and Hodge loci"

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[249] arXiv:2406.13546 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Dual of the Geometric Lemma and the Second Adjointness Theorem for $p$-adic reductive groups Show Chinese title

Title: $p$-阶约化群的几何引理对偶与第二个伴随定理

Kei Yuen Chan

Comments: 20 pages, comments welcome, v2: fixed some typos

Subjects: Representation Theory (math.RT) ; Number Theory (math.NT)

[250] arXiv:2406.13687 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: Diffraction of the primes and other sets of zero density Show Chinese title

Title: 素数和其他零密度集的衍射

Adam Humeniuk, Christopher Ramsey, Nicolae Strungaru

Comments: 37 pages, final version, accepted to Journal of the Australian Mathematical Society

Journal-ref: J. Aust. Math. Soc. 119 (2025) 202-245

Subjects: Functional Analysis (math.FA) ; Number Theory (math.NT)