The \(GL(3)\) Mellin transform for twisted non-cuspidal forms of higher level
type: Item
instance of: scholarly article
title: The \(GL(3)\) Mellin transform for twisted non-cuspidal forms of higher level
zbMATH Open document ID: 0924.11037
DOI: 10.1007/BF02783052
author: K. Appert
published in: Israel Journal of Mathematics
publication date: 1999-11-15T00:00:00Z
review text: This paper is devoted to the study of Dirichlet series whose coefficients are themselves essentially of the form \(\mu\mapsto L(s,\chi_{\mu^2})\) where \(\chi_{\mu^2}\) is the cubic residue character \(\text{mod } \mu^2\). The authors demonstrate that the Dirichlet series with twists can be represented as Mellin transforms of a residue of an Eisenstein series on the three-fold metaplectic cover of \(GL(3)\). They can prove both the analytic continuation and a `functional equation'; the latter involve, at least in a special case, a Dirichlet series where classical Kloosterman sums appear. They can also deduce asymptotic estimates for the average size of the \(L\)-functions. They quote this but defer the proof to a joint paper with \textit{J. Hoffstein}.
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 1270359
zbMATH Keywords: cubic residue character
zbMATH Keywords: Dirichlet series with twists
zbMATH Keywords: Mellin transforms
zbMATH Keywords: asymptotic estimates
zbMATH Keywords: average size
zbMATH Keywords: \(L\)-functions
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02783052
OpenAlex ID: W2080802571
description: scientific article; zbMATH DE number 1270359