An exponential sum involving Fourier coefficients of eigenforms for SL(2, Z)

被引：0

作者：

Acharya, Ratnadeep ^{[1
]}

Singh, Saurabh Kumar ^{[1
]}

机构：

[1] Indian Stat Inst, Stat Math Unit, 203 BT Rd, Kolkata 700108, W Bengal, India

来源：

RAMANUJAN JOURNAL | 2021年 / 54卷 / 03期

关键词：

Maass forms; Hecke eigenforms; Exponential sums; Vaughan's identity; OSCILLATIONS;

D O I：

10.1007/s11139-020-00255-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(f) (n) denote the normalized n-th Fourier coefficient of a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form for the full modular group. In this paper we shall exhibit cancellations in the following sum: (N<n <= 2)Sigma lambda(f) (n)nu(n)e(alpha n(theta)), where alpha, theta are real numbers with 0 < theta < 1 and nu(n) is either mu(n) or Lambda(n).

引用

页码：699 / 716

页数：18

共 19 条

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