Weight aspect exponential sums for Fourier coefficients of cusp forms
type: Item
instance of: scholarly article
title: Weight aspect exponential sums for Fourier coefficients of cusp forms
author: Fei Hou
published in: Monatshefte für Mathematik
publication date: 2022-10-18T00:00:00Z
review text: Let \(f\) be a primitive holomorphic cusp form of positive even weight \(k\) and denote its \(n\)-th Fourier coefficient by \(\lambda_f(n)\). The paper under review concerns about a uniform bound on the exponential sum of Fourier coefficients \(\lambda_f(n)\) with the twists. More precisely, the author studies the explicit dependence for the quadratic exponential sums, as a way to explore new behavior of the form in these types of sums. He aims to obtain an estimate in terms of the weight parameter. As an application of the main theorem, he obtains the explicit dependence on the weight aspect for the quadratic exponential sums involving Fourier coefficients of cusp forms at prime arguments. The proofs are mainly based on calculations through Voronoï-type summation formula, a Wilton-type bound, Bessel functions and the circle method.
reviewed by: İlker İnam
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 7603028
zbMATH Keywords: holomorphic cusp forms
zbMATH Keywords: explicit dependence
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: exponential sums
Wikidata QID: Q115606397
MaRDI profile type: Publication
full work available at URL: s00605-022-01750-w
OpenAlex ID: W4291009305
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DOI: 10.1007/S00605-022-01750-W
description: scientific article; zbMATH DE number 7603028