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

Let λ 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 N λ f ( n ) ν ( n ) e α n θ , where α , θ are real numbers with...

Full description

Saved in:
Bibliographic Details
Published in:The Ramanujan journal 2021-04, Vol.54 (3), p.699-716
Main Authors: Acharya, Ratnadeep, Singh, Saurabh Kumar
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Real numbers
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let λ 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 N λ f ( n ) ν ( n ) e α n θ , where α , θ are real numbers with 0 < θ < 1 , and ν ( n ) is either μ ( n ) or Λ ( n ) .
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00255-0