First moments of Fourier coefficients of GL(r) cusp forms

被引：6

作者：

Goldfeld, Dorian ^{[1
]}

Sengupta, Jyoti ^{[2
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] Tata Inst Fundamental Res, Bombay 400005, Maharashtra, India

来源：

JOURNAL OF NUMBER THEORY | 2016年 / 161卷

关键词：

L-functions; Cuspidal automorphic representation; Moments; SUMS; GL(N);

D O I：

10.1016/j.jnt.2014.12.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let pi be an irreducible cuspidal automorphic representation of GL(r, A) where r >= 2 and A is the adele ring of Q. Let a(pi) (n) denote the nth Dirichlet series coefficient of the L-function associated to pi. The main goal of this paper is to obtain strong bounds for the first moment Sigma(n <= x) a pi (n) as in x -> infinity. The bounds we obtain are better than all previously obtained bounds for the higher rank situation when r >= 3 and pi is not a symmetric power of a GL(2, A) cuspidal automorphic representation. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：435 / 443

页数：9

共 13 条

[1] FUNCTIONAL EQUATIONS WITH MULTIPLE GAMMA FACTORS AND AVERAGE ORDER OF ARITHMETICAL FUNCTIONS [J].