A note on the Fourier coefficients of Hecke-Maass forms

被引：4
|
作者：
Tang, Hengcai [1 ]
机构：
[1] Henan Univ, Sch Math & Informat Sci, Kaifeng 475004, Henan, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Fourier coefficients of cusp forms; Symmetric square L-function; Rankin-Selberg L-function; CUSP FORMS; SUMS;
D O I：
10.1016/j.jnt.2012.09.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
To a Hecke-Maass form f(z) with Laplace eigenvalue 1/4 + nu(2), we have an automorphic L-function L(s, sym(2) f) which is called the symmetric square L-function associated to f. Suppose that lambda(sym2) (f)(n) is the nth Fourier coefficient of L(s, sym(2) f). In this paper, the estimate Sigma(n <= x)lambda(sym2) f(n) << nu(3/4+epsilon)x(1/2+epsilon) + x(39/64+epsilon) is established. (C) 2012 Elsevier Inc. All rights reserved.
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页码：1156 / 1167
页数：12
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