Fourier coefficients at primes twisted with exponential functions

被引：1
|
作者：
Zhang, Wei [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2019年 / 201卷
基金：
中国国家自然科学基金;
关键词：
Fourier coefficients of cusp forms; Automorphic L-function; Zero-density; Exponential sums; ZERO-DENSITY ESTIMATE; OSCILLATIONS;
D O I：
10.1016/j.jnt.2019.02.018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let f (z) be a holomorphic normalized Hecke-eigen cusp form of weight kappa for SL2 (Z) with Fourier coefficients lambda(f) (n). In this paper, we estimate the sum of lambda(f) (n) at primes twisted with exponential functions e(alpha P-theta) for 0 < theta < 1. New upper bounds are proved for fixed alpha. Similar results are also given for the analogous situation of non-holomorphic forms. (C) 2019 Elsevier Inc. All rights reserved.
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页码：280 / 291
页数：12
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