The Rankin-Selberg method for non-holomorphic automorphic forms
type: Item
instance of: scholarly article
title: The Rankin-Selberg method for non-holomorphic automorphic forms
zbMATH Open document ID: 0840.11020
author: Yanyan Li
published in: Journal of Number Theory
publication date: 1996-07-01T00:00:00Z
review text: Let \(\Gamma\) be a Fuchsian group of the first kind, with at least one cusp. The author considers the Rankin-Selberg convolution for \(\Gamma\)-automorphic forms of arbitrary real weight. In this case, two types of Rankin-Selberg zeta-functions arise, corresponding to the Fourier coefficients at positive and negative indexes, respectively. The author proves the analytic continuation and a function equation for these zeta-functions. As an application he proves asymptotic formulas for the summatory function for the squares of the Fourier coefficients. The author uses methods which can also be found in earlier papers of the reviewer [Math. Z. 211, 155-172 (1992; Zbl 0778.11033), Acta Arith. 65, 1-14 (1993; Zbl 0790.11037)], where the same kind of results are obtained. The reviewer is somewhat surprised that the author should not have had knowledge about this.
reviewed by: Roland Matthes
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 749191
zbMATH Keywords: asymptotic formulas for summatory function
zbMATH Keywords: Fuchsian group
zbMATH Keywords: Rankin-Selberg convolution for \(\Gamma\)-automorphic forms
zbMATH Keywords: Rankin-Selberg zeta-functions
zbMATH Keywords: Fourier coefficients
MaRDI profile type: Publication
full work available at URL: jnth.1995.1035
OpenAlex ID: W1994588108
DOI: 10.1006/JNTH.1995.1035
description: scientific article; zbMATH DE number 749191