Estimates for sums of coefficients of Dirichlet series with functional equation
type: Item
instance of: scholarly article
title: Estimates for sums of coefficients of Dirichlet series with functional equation
zbMATH Open document ID: 1046.11031
DOI: 10.1023/A:1026251313579
author: V. Kumar Murty
published in: The Ramanujan Journal
publication date: 2004-01-06T00:00:00Z
review text: It is well known how to draw conclusions on the sum function of the coefficients of a Dirichlet series if it is known that this series satisfies a functional equation of the Riemann type. The author proves estimates for the sum function (also over an arithmetic progression) under stronger conditions such as the validity of a formula of the Rankin-Selberg type for the mean square of the coefficients, or supposing that the twists of the series with certain Dirichlet characters satisfy a functional equation.
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 2022029
zbMATH Keywords: Dirichlet series
zbMATH Keywords: functional equation
zbMATH Keywords: Fourier coefficients of modular forms
reviewed by: Matti Jutila
MaRDI profile type: Publication
full work available at URL: a:1026251313579
OpenAlex ID: W4237067778
description: scientific article; zbMATH DE number 2022029