Number Theory

Authors and titles for October 2025

[51] arXiv:2510.04387 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Sums of the floor function related to class numbers of imaginary quadratic fields Show Chinese title

Title: 与虚二次域类数相关的地板函数之和

Marc Chamberland, Karl Dilcher

Subjects: Number Theory (math.NT)

[52] arXiv:2510.04444 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A functional equation for multiple zeta functions and generalized confluent hypergeometric functions Show Chinese title

Title: 多个zeta函数和广义合流超几何函数的函数方程

Anju Yokoi

Subjects: Number Theory (math.NT)

[53] arXiv:2510.04708 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mock modular forms from the k-rank moments Show Chinese title

Title: 从k-阶矩中得到的模拟模形式

Kilian Rausch

Comments: 28 pages, comments welcome

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

[54] arXiv:2510.04799 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Divisibility among power GCD and power LCM matrices on certain gcd-closed sets Show Chinese title

Title: 某些GCD闭集上的幂GCD和幂LCM矩阵的可除性

Jixiang Wan, Guangyan Zhu

Subjects: Number Theory (math.NT)

[55] arXiv:2510.04805 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Serre weight conjectures for $\mathrm{GSp}_4$ Show Chinese title

Title: 塞尔权猜想对于$\mathrm{GSp}_4$

Daniel Le, Bao V. Le Hung, Heejong Lee

Comments: 36 pages. Comments are welcome!

Subjects: Number Theory (math.NT)

[56] arXiv:2510.04873 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums Show Chinese title

Title: 三维和四维中的傅里叶插值以及实变量Kloosterman和

Danylo Radchenko, Qihang Sun

Comments: We thank Professor Dr. Shparlinski for kindly pointing out our misuse of the bounds for sums of Kloosterman sums (in Sections 4 and 5). This has been corrected in the revised version v2

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

[57] arXiv:2510.05031 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Correction to "Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series" Show Chinese title

Title: "Kudla的模性猜想与形式傅里叶-雅可比级数"的更正

Jan Hendrik Bruinier, Martin Raum

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

[58] arXiv:2510.05248 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Lower bounds for counting $A_4$-quartic fields Show Chinese title

Title: 计数$A_4$-四次域的下界

Daniel Loughran, Ross Paterson

Comments: 24 pages, comments welcome!

Subjects: Number Theory (math.NT)

[59] arXiv:2510.05418 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The commutative algebra of congruence ideals and applications to number theory Show Chinese title

Title: 交换代数的同余理想及其在数论中的应用

Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning

Comments: 26 pages

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

[60] arXiv:2510.05427 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Joint distributions of error terms for primes in arithmetic progressions modulo 11 Show Chinese title

Title: 模11的算术级数中素数的误差项的联合分布

Kübra Benli, Greg Martin, Paul Péringuey

Comments: 24 pages

Subjects: Number Theory (math.NT)

[61] arXiv:2510.05448 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The inter-universal Teichmüller theory and new Diophantine results over rational numbers. II Show Chinese title

Title: 互异素数域的Teichmüller理论与有理数上的新丢番图结果。 II

Zhong-Peng Zhou

Subjects: Number Theory (math.NT)

[62] arXiv:2510.05462 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Multiplicative dependence in the denominators of points of elliptic curves Show Chinese title

Title: 椭圆曲线点分母中的乘法相关性

Attila Bérczes, Subham Bhakta, Lajos Hajdu, Alina Ostafe, Igor E. Shparlinski

Subjects: Number Theory (math.NT)

[63] arXiv:2510.05501 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Computing class groups and unit groups in Magma Show Chinese title

Title: 计算Magma中的类群和单位群

Andreas-Stephan Elsenhans, John Voight

Comments: 18 pages, 2 figures

Subjects: Number Theory (math.NT)

[64] arXiv:2510.05595 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Factorization of power GCD matrices and power LCM matrices on certain gcd-closed sets Show Chinese title

Title: 幂GCD矩阵和幂LCM矩阵在某些GCD闭包集上的分解

Guangyan Zhu, Yuanyuan Luo, Jixiang Wan

Subjects: Number Theory (math.NT)

[65] arXiv:2510.05602 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the ternary Estermann problem with almost proportional summands Show Chinese title

Title: 关于具有几乎成比例加数的三元Estermann问题

Firuz Rakhmonov

Comments: 14 pages

Journal-ref: Rakhmonov, F. Z. 2024, ''Asymptotic formula in generalization of ternary Esterman problem with almost proportional summands'' , Chebyshevskii sbornik, vol. 25, no. 4, pp. 120-137

Subjects: Number Theory (math.NT)

[66] arXiv:2510.05659 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Prime Geodesic Theorem for Arithmetic Compact Surfaces Show Chinese title

Title: 算术紧曲面的素测地线定理

Chenhao Tang, Han Wu, Jie Yang, Wenyan Yang

Subjects: Number Theory (math.NT)

[67] arXiv:2510.05737 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Moments of the zeros of Faber polynomials of the Miller basis Show Chinese title

Title: 米勒基底的法伯多项式的零点的矩

Adi Zilka

Comments: 17 pages, 1 figure

Subjects: Number Theory (math.NT)

[68] arXiv:2510.05929 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Vanishing Coefficients of q^{5n+r} and q^{7n+r} in Certain Infinite q-series Expansions Show Chinese title

Title: 某些无限q级数展开中q^{5n加r}和q^{7n+r}的消失系数

M.P. Thejitha, Anusree Anand, S.N. Fathima

Comments: 10 pages

Subjects: Number Theory (math.NT)

[69] arXiv:2510.06161 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Distribution of mixed character sums and extremal problems for Littlewood polynomials Show Chinese title

Title: 混合特征和的分布以及Littlewood多项式的极值问题

Jonathan W. Bober, Oleksiy Klurman, Besfort Shala

Comments: 34 pages

Subjects: Number Theory (math.NT) ; Classical Analysis and ODEs (math.CA) ; Complex Variables (math.CV) ; Probability (math.PR)

[70] arXiv:2510.06192 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Ratios of two powers of van der Laan-Padovan numbers Show Chinese title

Title: van der Laan-Padovan数的两个幂的比值

Tomohiro Yamada

Comments: 15 pages

Subjects: Number Theory (math.NT)

[71] arXiv:2510.06423 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mod-5 Galois images from abelian surfaces Show Chinese title

Title: 从阿贝尔曲面得到的模5伽罗瓦像

Aidan Hennessey, Mathilde Kermorgant, Andy Zhu

Comments: co-author emails: aidan.hennessey.gr@dartmouth.edu andy_zhu1@brown.edu

Subjects: Number Theory (math.NT)

[72] arXiv:2510.06520 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Products of Tribonacci Numbers that are the Products of Factorials Show Chinese title

Title: 三阶斐波那契数的乘积为阶乘的乘积

Pranabesh Das, J.C. Saunders

Subjects: Number Theory (math.NT)

[73] arXiv:2510.06523 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Continuation of Dirichlet series I Show Chinese title

Title: 狄利克雷级数的延续 I

Kevin Smith

Comments: In v3 an oversight in v2 is corrected, ensuring that linearity of the main result holds

Subjects: Number Theory (math.NT)

[74] arXiv:2510.06688 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Verification of Gilbraith's conjecture up to 10$^{14}$ Show Chinese title

Title: 吉尔布雷思猜想的验证至10$^{14}$

Simon Plouffe

Comments: Minor changes and addition of a new reference

Subjects: Number Theory (math.NT)

[75] arXiv:2510.06983 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Counting integral points in homogeneous spaces over function fields Show Chinese title

Title: 在函数域上的齐次空间中计数整数点

Sheng Chen, Jing Liu

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

[76] arXiv:2510.06993 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A remark on weighted average multiplicities in prime factorisation Show Chinese title

Title: 关于素因数分解中加权平均重数的备注

Viktor Mirjanić, Daattavya Aggarwal, Challenger Mishra

Comments: 19 pages, 5 figures

Subjects: Number Theory (math.NT)

[77] arXiv:2510.07046 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Brun's inequality for a geometric lattice Show Chinese title

Title: 布伦的不等式对于几何格

M. Ram Murty, Sunil Naik

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

[78] arXiv:2510.07056 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On divisibility of Hecke eigenvalues of Ikeda lifts Show Chinese title

Title: 关于伊克达提升的Hecke特征值的可除性

Sanoli Gun, Sunil Naik

Comments: To appear in Kyushu Journal of Mathematics

Subjects: Number Theory (math.NT)

[79] arXiv:2510.07168 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Solutions of a polynomial equation modulo a prime power Show Chinese title

Title: 多项式方程模素数幂的解

Arnaud Bodin, Christian Drouin

Comments: To appear in American Mathematical Monthly. The article comes with a "Sage" library, which you will find in the source files

Subjects: Number Theory (math.NT)

[80] arXiv:2510.07237 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: General Recurrence Multidimensional Zeckendorf Representations Show Chinese title

Title: 一般递归多维Zeckendorf表示

Jiarui Cheng, Steven J. Miller, Sebastian Rodriguez-Labastida, Tianyu Shen, Alan Sun, Garrett Tresch

Comments: 22 pages, 4 figures

Subjects: Number Theory (math.NT)

[81] arXiv:2510.07530 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A variant of Collatz's Conjecture over Binary Polynomials Show Chinese title

Title: 二进制多项式上的Collatz猜想变体

Luis H. Gallardo, Olivier Rahavandrainy

Subjects: Number Theory (math.NT)

[82] arXiv:2510.07577 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Markoff triples and Nielsen equivalence in $\text{SL}_2(\mathbb{F}_p)$ Show Chinese title

Title: 马尔可夫三元组和Nielsen等价在$\text{SL}_2(\mathbb{F}_p)$

Daniel E. Martin

Comments: 56 pages. Sage code for Algorithm 1 will be posted on the author's webpage: dem6.people.clemson.edu

Subjects: Number Theory (math.NT)

[83] arXiv:2510.07647 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The $n^{th}$ centered moments of a large orthogonal family of automorphic $L$-functions Show Chinese title

Title: 大正交自守$L$函数族的$n^{th}$中心矩

Vorrapan Chandee, Yoonbok Lee, Xiannan Li

Comments: 73 pages

Subjects: Number Theory (math.NT)

[84] arXiv:2510.07710 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Equidistribution of sequences associated with a-points of the derivatives of the Riemann zeta function Show Chinese title

Title: 与黎曼zeta函数导数的a点相关的序列的等分布性

Hideki Murahara, Tomokazu Onozuka

Subjects: Number Theory (math.NT)

[85] arXiv:2510.07769 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Strict Log-concavity of $k$-coloured Partitions Show Chinese title

Title: $k$-颜色分拆的严格对数凹性

Kathrin Bringmann, Ben Kane, Anubhab Pahari, Larry Rolen

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

[86] arXiv:2510.07787 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Minimal Denominators Lying in Subsets of the Ring of Polynomials over a Finite Field Show Chinese title

Title: 有限域上多项式环的子集中的最小分母

Noy Soffer Aranov

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

[87] arXiv:2510.07803 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Sums of Exponential Terms, Conserved Quantities, and the Real Wave Numbers Show Chinese title

Title: 指数项的和，守恒量和实波数

Terence R. Smith

Comments: 7 pages

Subjects: Number Theory (math.NT)

[88] arXiv:2510.07873 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the decimal digits of $1/p$ Show Chinese title

Title: 关于$1/p$的十进制数字

Kurt Girstmair

Subjects: Number Theory (math.NT)

[89] arXiv:2510.08486 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Twists arising from torsion points Show Chinese title

Title: 从扭点产生的扭结

Lukas Novak

Comments: 10 pages; comments welcome

Subjects: Number Theory (math.NT)

[90] arXiv:2510.08708 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On higher regulators of Picard modular surfaces Show Chinese title

Title: 关于佩卡德模表面的高阶调节子

Linli Shi

Comments: Based on the author's Ph.D. thesis at the University of Connecticut (2025); 100 pages. Comments welcome

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

[91] arXiv:2510.08760 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Further Investigation on Cyclotomic Mapping Permutation Polynomials over Finite Fields Show Chinese title

Title: 对有限域上分圆映射置换多项式的进一步研究

Suman Mondal

Comments: 9 pages

Subjects: Number Theory (math.NT)

[92] arXiv:2510.08786 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The p-adic distance of special points to subvarieties Show Chinese title

Title: 特殊点到子簇的p进距离

José Felipe Voloch

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

[93] arXiv:2510.08862 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An inverse theorem on sets with rich additive structure modulo primes Show Chinese title

Title: 模素数的具有丰富加法结构的集合的逆定理

Ernie Croot, Junzhe Mao, Chi Hoi Yip

Comments: 21 pages

Subjects: Number Theory (math.NT)

[94] arXiv:2510.08871 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Experimental investigations on Lehmer's conjecture for elliptic curves Show Chinese title

Title: 关于椭圆曲线Lehmer猜想的实验研究

Sven Cats, John Michael Clark, Charlotte Dombrowsky, Mar Curco Iranzo, Krystal Maughan, Eli Orvis

Comments: to appear in Proceedings of LuCaNT II

Subjects: Number Theory (math.NT)

[95] arXiv:2510.09005 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Note on large quadratic character sums Show Chinese title

Title: 关于大二次特征和的注记

Zikang Dong, Yutong Song, Ruihua Wang, Shengbo Zhao

Comments: 7 pages

Subjects: Number Theory (math.NT)

[96] arXiv:2510.09052 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Proof of the Genčev-Rucki Conjecture for Multiple Apéry-Like Series Show Chinese title

Title: 关于多重阿佩里类似级数的Genčev-Rucki猜想的证明

Ce Xu

Subjects: Number Theory (math.NT)

[97] arXiv:2510.09102 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Sum of short exponential sums with prime numbers Show Chinese title

Title: 短素数指数和的和

Firuz Rakhmonov

Subjects: Number Theory (math.NT)

[98] arXiv:2510.09356 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Fundamental domains for quaternionic S-arithmetic groups over totally real fields Show Chinese title

Title: 四元数S-算术群在全实域上的基本区域

Marc Masdeu, Eloi Torrents

Comments: 14 pages, comments welcome

Subjects: Number Theory (math.NT)

[99] arXiv:2510.09603 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Some new cases of Zilber-Pink in $Y(1)^3$ Show Chinese title

Title: 一些Zilber-Pink的新情况在$Y(1)^3$

Christopher Daw, Martin Orr, Georgios Papas

Comments: 29 pages; preliminary draft; comments welcome

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

[100] arXiv:2510.09954 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Local distribution of rational points in flag varieties Show Chinese title

Title: 旗流形中有理点的局部分布

Zhizhong Huang, Nicolas de Saxcé

Comments: 25 pages, 1 figure

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