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
收藏
页码：163 / 176
页数：14
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