Number Theory

Authors and titles for December 2020

[1] arXiv:2012.00178 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Counting integral points on some homogeneous varieties with large reductive stabilizers Show Chinese title

Title: 在具有大约化稳定子的某些齐次流形上计数整数点

Runlin Zhang

Comments: Correct a mistake made in the last section; main results unchanged; correct various typos; 20 pages

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

[2] arXiv:2012.00264 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: poly-Dedekind type DC sums involving poly-Euler functions Show Chinese title

Title: 多-Dedekind 类型 DC 和涉及多-Euler 函数

Yuankui Ma, Dae san Kim, Hyunseok Lee, Hanyoung Kim, Taekyun Kim

Comments: 16 pages

Subjects: Number Theory (math.NT)

[3] arXiv:2012.00285 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Connectors of the Ohno relation for parametrized multiple zeta series Show Chinese title

Title: 参数化多重Zeta级数的Ohno关系连接器

Hideki Murahara, Tomokazu Onozuka

Comments: 8 pages

Subjects: Number Theory (math.NT)

[4] arXiv:2012.00340 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On lower bounds of the dimensions of multizeta values in positive characteristic Show Chinese title

Title: 正特征下多重Zeta值维度的下界

Yen-Tsung Chen, Ryotaro Harada

Comments: 18 pages

Journal-ref: Doc. Math. (26), 537-559 (2021)

Subjects: Number Theory (math.NT)

[5] arXiv:2012.00502 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Determinants concerning Legendre symbols Show Chinese title

Title: 关于勒让德符号的行列式

Hai-Liang Wu

Comments: 7 pages

Subjects: Number Theory (math.NT)

[6] arXiv:2012.00539 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Zagier's weight $3/2$ mock modular form Show Chinese title

Title: 扎吉尔的权 $3/2$ 模块形式

Ajit Bhand, Ranveer Kumar Singh

Comments: A new lemma has been added, proofs of some of the lemmas have been corrected

Subjects: Number Theory (math.NT)

[7] arXiv:2012.00542 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On the Northcott property for special values of L-functions Show Chinese title

Title: 关于L函数特殊值的Northcott性质

Fabien Pazuki, Riccardo Pengo

Comments: 44 pages. Accepted for publication in the Revista Matem\'atica Iberoamericana

Journal-ref: Revista Matematica Iberoamericana, Vol. 40, No. 1 (2024)

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

[8] arXiv:2012.00570 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Kloosterman sums and Hecke polynomials in characteristics 2 and 3 Show Chinese title

Title: Kloosterman和在特征2和3中的Hecke多项式

C. Douglas Haessig

Comments: 6 pages

Subjects: Number Theory (math.NT)

[9] arXiv:2012.00603 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Fourier Analysis and the closed form for the Zeta Function at even positive integers Show Chinese title

Title: 傅里叶分析和黎曼ζ函数在正偶数处的闭合形式

Jibran Iqbal Shah

Comments: 6 pages, no figures. Comments welcome

Subjects: Number Theory (math.NT)

[10] arXiv:2012.00610 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Estimates of the bounds of $π(x)$ and $π((x+1)^{2})-π(x^{2})$ Show Chinese title

Title: $π(x)$和$π((x+1)^{2})-π(x^{2})$的边界估计

Connor Paul Wilson

Comments: 8 pages, 0 figures

Subjects: Number Theory (math.NT)

[11] arXiv:2012.00625 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Algebraicity of the near central non-critical value of symmetric fourth $L$-functions for Hilbert modular forms Show Chinese title

Title: 对Hilbert模形式的对称四次$L$-函数的近中心非临界值的代数性

Shih-Yu Chen

Subjects: Number Theory (math.NT)

[12] arXiv:2012.00882 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: The Generalized Superfactorial, Hyperfactorial and Primorial functions Show Chinese title

Title: 广义超阶乘、超阶乘和素数阶乘函数

Vignesh Raman

Subjects: Number Theory (math.NT)

[13] arXiv:2012.01041 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Infinitesimal characters in arithmetic families Show Chinese title

Title: 算术族中的无穷小特征

Gabriel Dospinescu, Vytautas Paškūnas, Benjamin Schraen

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

[14] arXiv:2012.01117 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Optimal spinor selectivity for quaternion Bass orders Show Chinese title

Title: 四元数Bass序的最佳旋量选择性

Deke Peng, Jiangwei Xue

Comments: 22 pages, made improvements and corrections, results unchanged

Subjects: Number Theory (math.NT)

[15] arXiv:2012.01147 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: The Manin-Drinfeld theorem and the rationality of Rademacher symbols Show Chinese title

Title: 曼宁-德林施泰因定理与雷姆斯彻符号的有理性

Claire Burrin

Comments: Corrects false statement (Proposition 4.4) in previous version. Added references and improved exposition. Comments welcome!

Journal-ref: Journal de th\'eorie des nombres de Bordeaux, Tome 34 (2022)

Subjects: Number Theory (math.NT)

[16] arXiv:2012.01202 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Simultaneous indivisibility of class numbers of pairs of real quadratic fields Show Chinese title

Title: 实二次域类数的同时不可分性

Jaitra Chattopadhyay, Anupam Saikia

Comments: Keywords and MSc classifications added. Minor modifications are made

Subjects: Number Theory (math.NT)

[17] arXiv:2012.01413 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Short effective intervals containing primes in arithmetic progressions and the seven cubes problem Show Chinese title

Title: 含素数的有效短区间与七个立方问题

Habiba Kadiri

Journal-ref: Mathematics of Computation 77 (2008), no. 263, 1733--1748

Subjects: Number Theory (math.NT)

[18] arXiv:2012.01423 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On some Féjer-type trigonometric sums Show Chinese title

Title: 关于某些Féjer型三角级数

R.B. Paris

Comments: 12 pages, 4 figures

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

[19] arXiv:2012.01534 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Artin-Schreier curves given by $\mathbb F_q$-linearized polynomials Show Chinese title

Title: 由$\mathbb F_q$-线性化多项式给出的 Artin-Schreier 曲线

Daniela Oliveira, F. E. Brochero Martínez

Subjects: Number Theory (math.NT) ; Discrete Mathematics (cs.DM)

[20] arXiv:2012.01677 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On the critical exponent for $k$-primitive sets Show Chinese title

Title: 关于$k$-原始集的临界指数

Tsz Ho Chan, Jared Duker Lichtman, Carl Pomerance

Comments: 14 pages

Journal-ref: Combinatorica (2021), 19 pp

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

[21] arXiv:2012.01712 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On the behavior of multiple zeta-functions with identical arguments on the real line I Show Chinese title

Title: 关于实线上具有相同参数的多重泽塔函数的行为 I

Kohji Matsumoto, Ilija Tanackov

Comments: 16pages, 9figures

Subjects: Number Theory (math.NT)

[22] arXiv:2012.01720 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On the behavior of multiple zeta-functions with identical arguments on the real line Show Chinese title

Title: 关于多重Zeta函数在实线上具有相同参数时的行为

Kohji Matsumoto, Toshiki Matsusaka, Ilija Tanackov

Comments: 26 pages, 12 figures. We combined two preprints (arXiv:2012.01712 and arXiv:2012.01720v1) into one article

Subjects: Number Theory (math.NT)

[23] arXiv:2012.01809 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Zeta functions over finite fields- An exposition of Dwork's methods Show Chinese title

Title: 有限域上的Zeta函数-Dwork方法的阐述

Martin Ortiz Ramirez

Comments: Old undergrad expository article

Subjects: Number Theory (math.NT)

[24] arXiv:2012.01844 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On effective $ε$-integrality in orbits of rational maps over function fields and multiplicative dependence Show Chinese title

Title: 关于函数域上有理映射轨道中的有效$ε$-整性以及乘法相关性

Jorge Mello

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

[25] arXiv:2012.01904 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Substitution maps in the Robba ring Show Chinese title

Title: 罗巴环中的替换映射

Laurent Berger

Comments: v2: added a result; v3 minor corrections; v4 final version, to appear in Ann Math Qu\'ebec (Perrin-Riou special issue)

Subjects: Number Theory (math.NT)

[26] arXiv:2012.01969 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials Show Chinese title

Title: 一个广义的Genocchi数及其对Bernoulli多项式的影响

Bakir Farhi

Comments: 12 pages

Subjects: Number Theory (math.NT)

[27] arXiv:2012.02078 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Extremal problems for GCDs Show Chinese title

Title: 极值问题关于GCDs

Ben Green, Aled Walker

Comments: One remark added

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

[28] arXiv:2012.02187 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Spectral aspect subconvex bounds for ${\rm U}_{n+1} \times {\rm U}_{n}$ Show Chinese title

Title: 谱方面子凸界对于${\rm U}_{n+1} \times {\rm U}_{n}$

Paul D. Nelson

Comments: 120 pages, 4 figures; to appear in Invent. Math. v4: minor corrections/clarifications, volume bounds formulated more generally

Subjects: Number Theory (math.NT) ; Analysis of PDEs (math.AP) ; Representation Theory (math.RT)

[29] arXiv:2012.02457 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Quantum modularity of partial theta series with periodic coefficients Show Chinese title

Title: 带有周期系数的部分θ级数的量子模性

Ankush Goswami, Robert Osburn

Comments: 16 pages, to appear in Forum Mathematicum

Journal-ref: Forum Mathematicum 33 (2021), no. 2, 451-463

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

[30] arXiv:2012.02503 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: A Cesàro average for an additive problem with an arbitrary number of prime powers and squares Show Chinese title

Title: 一个带有任意多个素数幂和平方数的加法问题的Cesàro平均

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

Comments: Added missing reference

Subjects: Number Theory (math.NT)

[31] arXiv:2012.02588 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Explicit Relations between Multiple Zeta Values and Related Variants Show Chinese title

Title: 多重Zeta值及其相关变体之间的显式关系

Ce Xu

Subjects: Number Theory (math.NT)

[32] arXiv:2012.03052 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Sequence elimination function and the formulas of prime numbers Show Chinese title

Title: 序列消去函数和素数公式

Ahmed Diab

Comments: 10 pages

Subjects: Number Theory (math.NT)

[33] arXiv:2012.03068 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Modules of Zeta Integrals for $\mathrm{GL}(1)$ Show Chinese title

Title: Zeta积分的模块对于$\mathrm{GL}(1)$

Gal Dor

Subjects: Number Theory (math.NT)

[34] arXiv:2012.03076 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Odoni's conjecture on arboreal Galois representations is false Show Chinese title

Title: 奥多尼关于树形伽罗瓦表示的猜想是错误的

Philip Dittmann, Borys Kadets

Comments: accepted manuscript version

Journal-ref: Proc. Amer. Math. Soc. 150 (2022), 3335-3343

Subjects: Number Theory (math.NT)

[35] arXiv:2012.03102 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: An effective analytic formula for the number of distinct irreducible factors of a polynomial Show Chinese title

Title: 一个多项式不同不可约因子数量的有效解析公式

Stephan Ramon Garcia, Ethan Simpson Lee, Josh Suh, Jiahui Yu

Comments: 15 pages

Subjects: Number Theory (math.NT)

[36] arXiv:2012.03523 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Wrońskian algebra and Broadhurst-Roberts quadratic relations Show Chinese title

Title: Wrońskian代数和Broadhurst-Roberts二次关系

Yajun Zhou

Comments: (v1) i+59 pages. Continuation of arXiv:1711.01829v2, reinterpretation and generalization of Fres\'an-Sabbah-Yu (arXiv:2005.11525v2, arXiv:2006.02702v1). (v2) i+55 pages. Notations upgraded and ancillary file updated. (v3) i+55 pages. For the penultimate paragraph in Sect. 4.2, there are minor notational changes and related updates in the ancillary file WronskianAlgebra_v3.nb

Journal-ref: Commun. Number Theory Phys. 15(4):651--741 (2021)

Subjects: Number Theory (math.NT) ; High Energy Physics - Theory (hep-th) ; Algebraic Geometry (math.AG)

[37] arXiv:2012.03771 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Combined Sieve Algorithm for Prime Gaps Show Chinese title

Title: 组合筛法算法求素数间隔

Seth Troisi

Comments: 10 pages, 4 figures, Open source code (GitHub), active development

Subjects: Number Theory (math.NT) ; Mathematical Software (cs.MS)

[38] arXiv:2012.03818 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Smallest common denominators for the homogeneous components of the Baker-Campbell-Hausdorff series Show Chinese title

Title: 齐次项的最小公分母的Baker-Campbell-Hausdorff级数

Harald Hofstätter

Subjects: Number Theory (math.NT)

[39] arXiv:2012.04013 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Relative Fontaine-Messing theory over power series rings Show Chinese title

Title: 幂级数环上的相对Fontaine-Messing理论

Tong Liu, Yong Suk Moon, Deepam Patel

Journal-ref: Int. Math. Res. Not. IMRN (2023)

Subjects: Number Theory (math.NT)

[40] arXiv:2012.04084 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Machine-Learning Arithmetic Curves Show Chinese title

Title: 机器学习算术曲线

Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver

Comments: 21 pages, 1 figure, 9 tables

Journal-ref: J. Symb. Comput. 115 (2023) 478-491

Subjects: Number Theory (math.NT) ; High Energy Physics - Theory (hep-th) ; Machine Learning (stat.ML)

[41] arXiv:2012.04139 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Diophantine equations with sum of cubes and cube of sum Show Chinese title

Title: 三次方的和与和的立方的不定方程

Bogdan A. Dobrescu, Patrick J. Fox

Comments: 36 pages. v2 contains new results, including: 1) any elliptic curve with certain torsion group is equivalent to cubic equation for some $a$; 2) number of primitive solutions is 0,1,2,3 or infinite; 3) for any integer $a$, if one primitive solution is known, then an infinite set of solutions can be generated. Version accepted by Communications in Number Theory and Physics, plus an appendix on $a=4$

Subjects: Number Theory (math.NT) ; High Energy Physics - Phenomenology (hep-ph) ; High Energy Physics - Theory (hep-th)

[42] arXiv:2012.04165 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*) Show Chinese title

Title: 关于Bessel函数的积分及其在Mahler测度中的应用（附录由J.S. Friedman*提供）

George Anton, Jessen A. Malathu, Shelby Stinson

Comments: To appear in the Bulletin of the Australian Mathematical Society; 12 pages, 4 figures

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

[43] arXiv:2012.04219 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Formal degrees and the local theta correspondence: the quaternionic case Show Chinese title

Title: 正式度与局部θ对应：四元数情形

Hirotaka Kakuhama

Comments: 68 pages

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

[44] arXiv:2012.04311 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Uniform bounds for norms of theta series and arithmetic applications Show Chinese title

Title: theta级数范数的统一界及算术应用

Fabian Waibel

Subjects: Number Theory (math.NT)

[45] arXiv:2012.04392 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Exceptional characters and nonvanishing of Dirichlet $L$-functions Show Chinese title

Title: 异常字符和狄利克雷$L$函数的非零性

H. M. Bui, Kyle Pratt, Alexandru Zaharescu

Comments: 37 pages. To appear in Mathematische Annalen

Subjects: Number Theory (math.NT)

[46] arXiv:2012.04508 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Equidistribution of primitive lattices in $\mathbb{R}^n$ Show Chinese title

Title: 原始格在$\mathbb{R}^n$中的等分布

Tal Horesh, Yakov Karasik

Subjects: Number Theory (math.NT)

[47] arXiv:2012.04523 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Congruences concerning generalized central trinomial coefficients Show Chinese title

Title: 关于广义中心三项系数的同余式

Jia-Yu Chen, Chen Wang

Comments: 13 pages. This is a preliminary manuscript

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

[48] arXiv:2012.04615 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Derangements and the $p$-adic incomplete gamma function Show Chinese title

Title: 错位排列和$p$-进制不完全伽马函数

Andrew O'Desky, David Harry Richman

Comments: 26 pages; new material on m-values; revised for clarity

Journal-ref: Trans. Amer. Math. Soc. 376 (2023), 1065-1087

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

[49] arXiv:2012.04693 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Vojta's conjecture, heights associated with subschemes, and primitive prime divisors in arithmetic dynamics Show Chinese title

Title: 瓦杰塔猜想、与子概形相关的高度以及算术动力学中的原始素数因子

Yohsuke Matsuzawa

Comments: 30 pages

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

[50] arXiv:2012.04695 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Short paths in PU(2) Show Chinese title

Title: PU(2)中的短路径

Zachary Stier

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