Estimates for sums of coefficients of Dirichlet series with functional equation

被引：1

作者：

Murty, VK ^{[1
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada

来源：

RAMANUJAN JOURNAL | 2003年 / 7卷 / 1-3期

关键词：

Dirichlet series; functional equation; Fourier coefficients of modular forms;

D O I：

10.1023/A:1026251313579

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose we have a Dirichlet series L(s)=Sigma(n=1)(infinity) a(n)n(-s) such that it, and its twists by Dirichlet characters have analytic continuation and a functional equation of a specific kind. Suppose also that the root numbers of the twists are equidistributed on the unit circle. The purpose of this note is to get an estimate for the quantity [GRAPHICS] for a prime modulus p. We use a modification of the method of Chandrasekharan and Narasimhan and we use in an essential way a Rankin-Selberg type estimate for the average of \a(n)\(2).

引用

页码：223 / 233

页数：11

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