The Average Behaviors of the Fourier Coefficients of j-th Symmetric Power L-Function over Two Sparse Sequences of Positive Integers

被引：3

作者：

Liu, Huafeng ^{[1
]}

Yang, Xiaojie ^{[1
]}

机构：

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

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2024年 / 50卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Fourier coefficients; j-th symmetric L-function; Dirichlet character; CUSP FORMS; MOMENT; SUM;

D O I：

10.1007/s41980-023-00850-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that x is a sufficiently large number and j >= 2 is any integer. Let L(s,sym(j)f) be the j-th symmetric power L-function associated with the primitive holomorphic cusp form f of weight k for the full modular group SL2(Z). Also, let lambda(symjf)(n) be the n-th normalized Dirichlet coefficient of L(s,sym(j)f). In this paper, we establish asymptotic formulas for sums of Dirichlet coefficients lambda(symjf)(n) over two sparse sequences of positive integers, which improves previous results.

引用

页数：16

共 8 条

[1] ON THE AVERAGE BEHAVIOR OF THE FOURIER COEFFICIENTS OF jTH SYMMETRIC POWER L-FUNCTION OVER CERTAIN SEQUENCES OF POSITIVE INTEGERS
Sharma, Anubhav
Sankaranarayanan, Ayyadurai
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2023, 73 (03) : 885 - 901
[2] On the average behavior of the Fourier coefficients of jth symmetric power L-function over certain sequences of positive integers
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Ayyadurai Sankaranarayanan
Czechoslovak Mathematical Journal, 2023, 73 : 885 - 901
[3] A note on average behaviour of the Fourier coefficients of jth symmetric power L-function over certain sparse sequence of positive integers
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CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024, 74 (02) : 623 - 636
[4] On the second moment of Fourier coefficients of symmetric power L-function
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INTERNATIONAL JOURNAL OF NUMBER THEORY, 2025,
[5] Fourier coefficients of the triple product L-function over sparse sets
Yao, Weili
RAMANUJAN JOURNAL, 2025, 66 (01): : 1 - 16
[6] Average behaviour of Fourier coefficients of j-symmetric power L-functions over some polynomials
Sarkar, A.
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ACTA MATHEMATICA HUNGARICA, 2024, 174 (01) : 75 - 93
[7] On a general divisor problem associated to coefficients of Rankin-Selberg L-functions over a sparse set of sequences of positive integers
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RAMANUJAN JOURNAL, 2025, 66 (01): : 38 - 38
[8] Average behaviour of Fourier coefficients of j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}-symmetric power L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document}-functions over some polynomials
A. Sarkar
M. Shahvez Alam
Acta Mathematica Hungarica, 2024, 174 (1) : 75 - 93

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