Number Theory

Authors and titles for October 2025

[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)