Sums of coefficients of general L-functions over arithmetic progressions and applications

被引：0

作者：

Wang, Dan ^{[1
]}

机构：

[1] Qilu Univ Technol, Shandong Acad Sci, Sch Math & Stat, Jinan 250353, Shandong, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 265卷

关键词：

Fourier coefficients; Arithmetic progression; Cusp forms; FOURIER COEFFICIENTS; EULER PRODUCTS; CLASSIFICATION;

D O I：

10.1016/j.jnt.2024.06.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the asymptotic distribution of coefficients of general L-functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for Gamma = SL(2, Z) over arithmetic progressions, and improve the results of Jiang and L & uuml; [10]. Our new results remove the restriction to prime module and improve the interval length of module q. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：117 / 137

页数：21

共 50 条

[21] A NOTE ON THE COEFFICIENTS OF POWER SUMS OF ARITHMETIC PROGRESSIONS br
Cereceda, Jose L.
MISKOLC MATHEMATICAL NOTES, 2022, 23 (02) : 551 - 557
[22] ON EXPONENTIAL SUMS INVOLVING COEFFICIENTS OF L-FUNCTIONS FOR SL(3, Z) OVER PRIMES
Hou, Fei
Jiang, Yujiao
Lu, Guangshi
QUARTERLY JOURNAL OF MATHEMATICS, 2016, 67 (02): : 285 - 301
[23] On character sums and exponential sums over generalized arithmetic progressions
Shao, Xuancheng
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2013, 45 : 541 - 550
[24] On comparing the coefficients of general product L-functions
Hua, Guodong
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024,
[25] On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class
Bui, H. M.
Keating, J. P.
Smith, D. J.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 94 : 161 - 185
[26] Summation formulae of multiplicative functions over arithmetic progressions and applications
Jiang, Yujiao
Lue, Guangshi
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2024,
[27] Uniform estimates for sums of coefficients of symmetric power L-functions
Guohua Chen
Xiaoguang He
Lithuanian Mathematical Journal, 2022, 62 : 421 - 434
[28] Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions
Guangshi Lü
Qiang Ma
Monatshefte für Mathematik, 2024, 204 : 127 - 155
[29] Uniform estimates for sums of coefficients of symmetric power L-functions
Chen, Guohua
He, Xiaoguang
LITHUANIAN MATHEMATICAL JOURNAL, 2022, 62 (04) : 421 - 434
[30] L-functions of exponential sums on curves over rings
Blache, Regis
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (03) : 345 - 359

← 1 2 3 4 5 →