Oscillations of Fourier coefficients of cusp forms over primes

被引：3

作者：

Hou, Fei ^{[1
]}

Lu, Guangshi ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2016年 / 159卷

关键词：

Exponential sums; Fourier coefficient; Cusp form; EXPONENTIAL-SUMS;

D O I：

10.1016/j.jnt.2015.07.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a primitive holomorphic or Maass cusp form for the group SL(2,Z), and a(f)(n) its nth normalized Fourier coefficient. It is proved that, for any alpha,beta is an element of R, there exists an effective positive constant c such that Sigma(n <= N) Lambda(n)a(f()n)e(alpha n(2) + beta n) <<(f) N exp(-c root log N). (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：370 / 383

页数：14

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