Shifted convolution sums involving theta series

被引：1

作者：

Sun, Qingfeng ^{[1
]}

机构：

[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China

来源：

RAMANUJAN JOURNAL | 2017年 / 44卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Shifted convolution sum; Cuspidal newform; Theta series; SELBERG L-FUNCTIONS; EQUIDISTRIBUTION;

D O I：

10.1007/s11139-017-9900-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a cuspidal newform (holomorphic orMaass) of arbitrary level and nebentypus and denote by lambda f (n) its nth Hecke eigenvalue. Let r(n) = # { (n(1),n(2)) is an element of Z(2) : n(1)(2) + n(2)(2) =n } . In this paper, we study the shifted convolution sum S-h(X) = Sigma lambda f(n+h)r(n), 1 <= h <= X, n <= X and establish uniform bounds with respect to the shift h for S-h(X).

引用

页码：13 / 36

页数：24

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