The \(GL(3)\) Rankin-Selberg convolution for functions not of rapid decay
type: Item
instance of: scholarly article
title: The \(GL(3)\) Rankin-Selberg convolution for functions not of rapid decay
zbMATH Open document ID: 0779.11021
DOI: 10.1215/S0012-7094-93-06911-6
author: Daniel Lieman
published in: Duke Mathematical Journal
publication date: 1994-01-23T00:00:00Z
review text: The Rankin-Selberg method has been studied in great generality in a large number of cases when the automorphic forms involved are cuspidal, i.e. of rapid decay. Only in the case \(GL_ 2\) this method was worked out (independently) by Patterson and Zagier for functions which are not of rapid decay. In this paper this theme is taken up in the case \(GL_ 3\). It gives a result for the Rankin-Selberg convolution of a \(GL_ 3(\mathbb{C})\) noncuspidal automorphic form with the maximal parabolic \(GL_ 3(\mathbb{R})\) Eisenstein series. In this case, the proof that the convolution evaluates to the correct Dirichlet series is almost identical to the proof in the case of a cusp form. The main task left is to determine the analytic behavior of the convolution.
reviewed by: Joachim Schwermer
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F12
zbMATH DE Number: 179237
zbMATH Keywords: \(GL(3)\) Rankin-Selberg convolution
zbMATH Keywords: noncuspidal automorphic form
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 179237