Number Theory

Authors and titles for January 2024

[1] arXiv:2401.00181 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the existence of Minkowski units Show Chinese title

Title: 关于闵可夫斯基单位的存在性

David Burns, Donghyeok Lim, Christian Maire

Subjects: Number Theory (math.NT)

[2] arXiv:2401.00215 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On families of elliptic curves $E_{p,q}:y^2=x^3-pqx$ that intersect the same line $L_{a,b}:y=\frac{a}{b}x$ of rational slope Show Chinese title

Title: 关于与具有有理斜率的直线 $E_{p,q}:y^2=x^3-pqx$ 相交的椭圆曲线族 $L_{a,b}:y=\frac{a}{b}x$

Eldar Sultanow, Malik Amir, Anja Jeschke, Amir Darwish Tfiha, Madjid Tehrani, William J Buchanan

Comments: 16 pages, 7 figures

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

[3] arXiv:2401.00270 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A number-theoretic problem concerning pseudo-real Riemann surfaces Show Chinese title

Title: 关于伪实黎曼曲面的一个数论问题

Gareth A. Jones, Alexander K. Zvonkin

Comments: 20 pages

Subjects: Number Theory (math.NT)

[4] arXiv:2401.00358 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Joint distribution in residue classes of families of polynomially-defined multiplicative functions Show Chinese title

Title: 多项式定义的乘法函数族在剩余类中的联合分布

Akash Singha Roy

Comments: 66 pages

Subjects: Number Theory (math.NT)

[5] arXiv:2401.00462 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the existence of analytic families of G-stable lattices and their reductions Show Chinese title

Title: 关于解析族 G-稳定格及其约化的存在性

Emiliano Torti

Subjects: Number Theory (math.NT)

[6] arXiv:2401.00537 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Anisotropy of quadratic forms over a global field of odd characteristic is diophantine Show Chinese title

Title: 具有奇特征的全局域上的二次型的各向异性是丢番图的

Guang Hu

Subjects: Number Theory (math.NT)

[7] arXiv:2401.00614 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Nontrivial Winning and Losing Parameters of Schmidt Games Show Chinese title

Title: 关于施密特博弈的非平凡获胜与失败参数

Vasiliy Neckrasov, Eric Zhan

Comments: Some issues are corrected // 21 pages, 7 figures

Subjects: Number Theory (math.NT)

[8] arXiv:2401.00630 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: An almost linear time algorithm testing whether the Markoff graph modulo $p$ is connected Show Chinese title

Title: 一个几乎线性时间的算法，用于测试模$p$的 Markoff 图是否连通

Colby Austin Brown

Comments: Version 3: Present more data and fix typos

Subjects: Number Theory (math.NT)

[9] arXiv:2401.00774 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Reciprocity formulas for certain generalized Hardy-Berndt sums Show Chinese title

Title: 关于某些广义Hardy-Berndt和的互惠公式

Yuan He

Subjects: Number Theory (math.NT)

[10] arXiv:2401.00892 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Joint distribution in residue classes of families of polynomially-defined additive functions Show Chinese title

Title: 多项式定义的加性函数族在剩余类中的联合分布

Akash Singha Roy

Comments: 34 pages

Subjects: Number Theory (math.NT)

[11] arXiv:2401.00982 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A note on odd partition numbers Show Chinese title

Title: 关于奇划分数的一个注记

Michael Griffin, Ken Ono

Comments: Corrects minor typos found by the referees

Subjects: Number Theory (math.NT)

[12] arXiv:2401.01000 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the real zeros of depth 1 quasimodular forms Show Chinese title

Title: 关于深度1拟模形式的实零点

Bo-Hae Im, Wonwoong Lee

Comments: 19 pages, 1 figure

Subjects: Number Theory (math.NT)

[13] arXiv:2401.01057 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A reciprocity relation for the twisted second moment of the Riemman Zeta function Show Chinese title

Title: 关于黎曼zeta函数扭曲二阶矩的互反关系

Rizwanur Khan

Subjects: Number Theory (math.NT)

[14] arXiv:2401.01137 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Three term rational function progressions in finite fields Show Chinese title

Title: 有限域中的三项有理函数序列

Guo-Dong Hong, Zi Li Lim

Comments: 17 pages

Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) ; Classical Analysis and ODEs (math.CA) ; Combinatorics (math.CO)

[15] arXiv:2401.01282 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Hilbert Poincaré series and kernels for products of $L$-functions Show Chinese title

Title: Hilbert-Poincaré级数和$L$-函数乘积的核

Mingkuan Zhang, Yichao Zhang

Subjects: Number Theory (math.NT)

[16] arXiv:2401.01293 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Bounds on the number of squares in recurrence sequences Show Chinese title

Title: 递推序列中平方数的界限

Paul M Voutier

Comments: Published version plus corrections (see last section)

Journal-ref: Journal of Number Theory, volume 265 (2024), 291--343

Subjects: Number Theory (math.NT)

[17] arXiv:2401.01348 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the upper and lower bound orders of almost prime triples Show Chinese title

Title: 关于几乎素数三元组的上下界顺序

Runbo Li

Comments: 12 pages

Subjects: Number Theory (math.NT)

[18] arXiv:2401.01351 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type II Show Chinese title

Title: 关于涉及特殊类型II素数的$\sqrt{p}$模一分布的一个注记

Runbo Li

Comments: 5 pages. Version 1 is I in this series

Subjects: Number Theory (math.NT)

[19] arXiv:2401.01355 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On sums of unequal powers of primes and powers of 2 Show Chinese title

Title: 关于不相等次幂的素数与2的次幂之和

Yuhui Liu

Subjects: Number Theory (math.NT)

[20] arXiv:2401.01365 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Non-isogenous superelliptic jacobians II Show Chinese title

Title: 非同源的超椭圆雅可比 II

Yuri G. Zarhin

Comments: 19 pages. arXiv admin note: substantial text overlap with arXiv:2204.10567

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

[21] arXiv:2401.01372 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Hopf algebras for the shuffle algebra and fractions from multiple zeta values Show Chinese title

Title: Hopf代数用于洗牌代数和多重泽塔值的分数

Li Guo, Wenchuan Hu, Hongyu Xiang, Bin Zhang

Subjects: Number Theory (math.NT) ; Mathematical Physics (math-ph)

[22] arXiv:2401.01385 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions Show Chinese title

Title: 关于雅可比椭圆函数的伯恩特型积分和级数

Ce Xu, Jianqiang Zhao

Comments: arXiv admin note: text overlap with arXiv:2311.15666

Subjects: Number Theory (math.NT)

[23] arXiv:2401.01435 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Nilpotent polynomials over $\mathbb{Z}$ Show Chinese title

Title: 幂零多项式关于$\mathbb{Z}$

Sayak Sengupta

Comments: 23 pages in total. This is a continuation of the research done by the author in the paper "Locally nilpotent polynomials over $\mathbb{Z}$". Comments are welcome!

Subjects: Number Theory (math.NT)

[24] arXiv:2401.01556 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the error term in a mixed moment of L-functions Show Chinese title

Title: 关于L-函数混合矩的误差项

Rizwanur Khan, Zeyuan Zhang

Comments: Mathematika 69 (2023), no. 3, 573--583

Subjects: Number Theory (math.NT)

[25] arXiv:2401.01803 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Sharp density discrepancy for cut and project sets: An approach via lattice point counting Show Chinese title

Title: 投影集的密度不一致性：通过点阵计数的方法

Henna Koivusalo, Jean Lagacé, Michael Björklund, Tobias Hartnick

Comments: The paper, authored by H. Koivusalo and J. Lagac\'e, includes an appendix by M. Bj\"orklund and T. Hartnick. 32 pages. Updated exposition

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

[26] arXiv:2401.01819 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Arithmetic progression in a finite field with prescribed norms Show Chinese title

Title: 有限域中的具有指定范数的算术级数

Kaustav Chatterjee, Hariom Sharma, Aastha Shukla, Shailesh Kumar Tiwari

Subjects: Number Theory (math.NT)

[27] arXiv:2401.01859 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: A spectral theorem for compact representations and non-unitary cusp forms Show Chinese title

Title: 紧表示和非么正尖形式的谱定理

Anton Deitmar

Subjects: Number Theory (math.NT)

[28] arXiv:2401.01860 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Reciprocity obstructions in semigroup orbits in SL(2, Z) Show Chinese title

Title: 半群轨道在 SL(2, Z) 中的互惠障碍

James Rickards, Katherine E. Stange

Comments: 28 pages, incorporated referee feedback

Subjects: Number Theory (math.NT)

[29] arXiv:2401.01892 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mean-square values of the Riemann zeta function on arithmetic progressions Show Chinese title

Title: 算术 progression 上的黎曼 zeta 函数的均方值

Hirotaka Kobayashi

Comments: This is an updated version of arXiv:2212.06520. 14 pages

Subjects: Number Theory (math.NT)

[30] arXiv:2401.02067 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Two improvements in Brauer's theorem on forms Show Chinese title

Title: 关于型的布劳尔定理的两项改进

Arthur Bik, Jan Draisma, Andrew Snowden

Comments: 22 pages

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

[31] arXiv:2401.02182 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Construction of Jacobi forms using adjoint of Jacobi-Serre derivative Show Chinese title

Title: 利用Jacobi-Serre导数的伴随构造Jacobi形式

Mrityunjoy Charan, Lalit Vaishya

Comments: 19 pages, comments and suggestions are welcome

Subjects: Number Theory (math.NT)

[32] arXiv:2401.02210 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Roth-type Theorem for high-power system in Piatetski-Shapiro primes (II) Show Chinese title

Title: 关于Piatetski-Shapiro素数中高次幂系统的Roth型定理（II）

Xiumin Ren, Yu-chen Sun, Qingqing Zhang, Rui Zhang

Comments: 14 pages

Subjects: Number Theory (math.NT)

[33] arXiv:2401.02346 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An Elementary Approach to the Group Law on Elliptic Curves Show Chinese title

Title: 椭圆曲线群律的一个初等方法

Sander Zwegers

Comments: 6 pages, extended and updated

Subjects: Number Theory (math.NT)

[34] arXiv:2401.02382 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Hilbert modular forms and Galois representations Show Chinese title

Title: 希尔伯特模形式与伽罗瓦表示

Ajith Nair, Ajmain Yamin

Comments: 30 pages. This article will be published in the second trimester proceedings of the yearlong program on 'Triangle groups, Belyi uniformisation and Modularity' organized by Bhaskaracharya Pratishthana, Pune in 2021-22

Subjects: Number Theory (math.NT)

[35] arXiv:2401.02657 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The integer group determinants for GA(1,p) and related semidirect products Show Chinese title

Title: 关于 GA(1,p) 及相关半直积的整数群行列式

Humberto Bautista Serrano, Bishnu Paudel, Chris Pinner

Subjects: Number Theory (math.NT)

[36] arXiv:2401.02741 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The sup-norm problem for newforms of large level on $\operatorname{PGL}(n)$ Show Chinese title

Title: 关于$\operatorname{PGL}(n)$上大水平的新形式的上确界范数问题

Radu Toma

Comments: 46 pages

Subjects: Number Theory (math.NT)

[37] arXiv:2401.02747 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Counting and Joint equidistribution of approximates Show Chinese title

Title: 计数与近似值的联合等分布

Gaurav Aggarwal, Anish Ghosh

Comments: This is a substantial revision. We have expanded and improved the exposition, and removed parts which discuss best approximations. These are now part of a separate paper "A Generalized L\'{e}vy-Khintchine Theorem". 43 pages, comments welcome!

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

[38] arXiv:2401.02813 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Estimates for the number of zeros of shifted combinations of completed Dirichlet series Show Chinese title

Title: 关于平移组合的完备Dirichlet级数零点个数的估计

Pedro Ribeiro

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

[39] arXiv:2401.02820 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quasi-Jacobi forms, Appell-Lerch functions, and false theta functions as q-brackets of functions on partitions Show Chinese title

Title: 拟雅可比形式、阿佩尔-莱尔奇函数和虚假θ函数作为分区函数的q括号

Kathrin Bringmann, Jan-Willem van Ittersum, Jonas Kaszian

Comments: 19 pages, improved exposition and presentation

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

[40] arXiv:2401.02922 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Computation of Fourier coefficients of automorphic forms of type $G_2$ Show Chinese title

Title: 傅里叶系数的计算——自守形式类型$G_2$

Aaron Pollack

Subjects: Number Theory (math.NT)

[41] arXiv:2401.02946 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Non-Noetherian Iwasawa Theory Show Chinese title

Title: 关于非诺特型伊瓦拉瓦理论

David Burns, Alexandre Daoud, Dingli Liang

Comments: 20 pages

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

[42] arXiv:2401.03091 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A single source theorem for primitive points on curves Show Chinese title

Title: 关于曲线上的本原点的单源定理

Maleeha Khawaja, Samir Siksek

Journal-ref: Forum of Mathematics, Sigma 13 (2025) e6

Subjects: Number Theory (math.NT)

[43] arXiv:2401.03099 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The modular approach to Diophantine equations over totally real fields Show Chinese title

Title: 全实数域上丢番图方程的模性方法

Maleeha Khawaja, Samir Siksek

Subjects: Number Theory (math.NT)

[44] arXiv:2401.03213 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Two formulas for certain double and multiple polylogarithms in two variables Show Chinese title

Title: 二变量的某些双及多重对数函数的两个公式

Masanobu Kaneko, Hirofumi Tsumura

Comments: 11 pages

Subjects: Number Theory (math.NT)

[45] arXiv:2401.03252 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: New Lower Bounds for the Schur-Siegel-Smyth Trace Problem Show Chinese title

Title: 新的施鲁尔-西格尔-斯迈思迹问题下界

Bryce Joseph Orloski, Naser Talebizadeh Sardari, Alexander Smith

Comments: First published in Mathematics of Computation in 2024, published by the American Mathematical Society

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

[46] arXiv:2401.03278 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Bounds on tree distribution in number theory Show Chinese title

Title: 数论中关于树分布的界限

Roberto Conti, Pierluigi Contucci, Vitalii Iudelevich

Comments: 28 pages, 1 figure

Subjects: Number Theory (math.NT)

[47] arXiv:2401.03380 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mordell--Tornheim Zeta Values, Their Alternating Version, and Their Finite Analogs Show Chinese title

Title: 莫德尔-托恩海姆泽塔值、它们的交错版本以及有限模拟

Crystal Wang, Jianqiang Zhao

Comments: 13 pages

Subjects: Number Theory (math.NT)

[48] arXiv:2401.03439 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Big Heegner points, generalized Heegner classes and $p$-adic $L$-functions in the quaternionic setting Show Chinese title

Title: 大Heegner点，广义Heegner类和四元数背景下的$p$-adic $L$-函数

Matteo Longo, Paola Magrone, Eduardo Rocha Walchek

Subjects: Number Theory (math.NT)

[49] arXiv:2401.03645 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the regularized products of some Dirichlet series Show Chinese title

Title: 关于某些 Dirichlet 级数的正则乘积

Mounir Hajli

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

[50] arXiv:2401.03663 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Congruence properties modulo prime powers for a class of partition functions Show Chinese title

Title: 关于一类分区函数对于素数幂的同余性质

Matthew Boylan, Swati

Comments: 22 pages

Subjects: Number Theory (math.NT)