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)