On Hecke eigenvalues at Piatetski-Shapiro primes

被引：5

作者：

Baier, Stephan ^{[1
]}

Zhao, Liangyi ^{[2
]}

机构：

[1] Jacobs Univ, Sch Sci & Engn, D-28725 Bremen, Germany

[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 81卷

关键词：

NUMBER THEOREM; EXPONENTIAL-SUMS; COEFFICIENTS; MONOMIALS;

D O I：

10.1112/jlms/jdp064

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(n) be the normalized nth Fourier coefficient of a holomorphic cusp form for the full modular group. We show that, for some constant C > 0 depending on the cusp form and every fixed c in the range 1 < c < 8/7, the mean value of lambda(p) is O (exp (-C root log N)) as p runs over all (Piatetski-Shapiro) primes of the form [n(c)] with n is an element of N and n <= N.

引用

页码：175 / 201

页数：27

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