Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions

被引：0

作者：

Han, Xue ^{[1
]}

Liu, Huafeng ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Shandong, Peoples R China

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2024年 / 64卷 / 02期

基金：

中国国家自然科学基金;

关键词：

cusp forms; Fourier coefficients; symmetric power L-function; FOURIER COEFFICIENTS; SUMS;

D O I：

10.1007/s10986-024-09636-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let m >= 2 be an integer. Let f be a holomorphic Hecke eigenform of even weight k for the full modular group SL(2, Z). Denote by lambda(m)(Sym)(f) (n) the nth normalized Dirichlet coefficient of the corresponding symmetric power L-function L(s, Sym(m) (f)) related to f. In this paper, we study the average behavior of the second moment of the Dirichlet coefficients lambda(m)(Sym)(f) (n) and establish its asymptotic formula.

引用

页码：163 / 176

页数：14

共 50 条

[31] The second moment of symmetric square L-functions over Gaussian integers
Balkanova, Olga
Frolenkov, Dmitry
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2022, 152 (01) : 54 - 80
[32] The Average Behavior of Fourier Coefficients of Symmetric Power L-Functions
Liu, Huafeng
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2023, 46 (06)
[33] The Average Behavior of Fourier Coefficients of Symmetric Power L-Functions
Huafeng Liu
Bulletin of the Malaysian Mathematical Sciences Society, 2023, 46
[34] The third moment of quadratic Dirichlet L-functions
Young, Matthew P.
SELECTA MATHEMATICA-NEW SERIES, 2013, 19 (02): : 509 - 543
[35] THE EIGHTH MOMENT OF DIRICHLET L-FUNCTIONS II
Chandee, Vorrapan
Li, Xiannan
Matomaki, Kaisa
Radziwill, Maksym
DUKE MATHEMATICAL JOURNAL, 2024, 173 (18) : 3453 - 3493
[36] The fourth moment of quadratic Dirichlet L-functions
Shen, Quanli
MATHEMATISCHE ZEITSCHRIFT, 2021, 298 (1-2) : 713 - 745
[37] On sign changes of the Fourier coefficients of symmetric power L-functions
Liu, Huafeng
Liu, Rui
JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2024, 39 (04)
[38] Mean Square Estimates for Coefficients of Symmetric Power L-Functions
Huixue Lao
Acta Applicandae Mathematicae, 2010, 110 : 1127 - 1136
[39] Mean Square Estimates for Coefficients of Symmetric Power L-Functions
Lao, Huixue
ACTA APPLICANDAE MATHEMATICAE, 2010, 110 (03) : 1127 - 1136
[40] Uniform estimates for sums of coefficients of symmetric power L-functions
Chen, Guohua
He, Xiaoguang
LITHUANIAN MATHEMATICAL JOURNAL, 2022, 62 (04) : 421 - 434

← 1 2 3 4 5 →