Periods of Eisenstein series: the Galois case
type: Item
instance of: scholarly article
title: Periods of Eisenstein series: the Galois case
zbMATH Open document ID: 1037.11033
DOI: 10.1215/S0012-7094-03-12016-5
author: Erez Lapid
author: Jonathan Rogawski
published in: Duke Mathematical Journal
publication date: 2004-01-28T00:00:00Z
review text: In this paper the periods of Eisenstein series are studied in the following case. Let \(H\) be a connected reductive group over a number field \(F\) and let \(G = \text{Res}_{E/F}\,H\), where \(E/F\) is a quadratic extension. The period of an automorphic form on \(G\) with respect to \(H\) is defined as a regularized integral. The main result of the paper is an expression for the period of a cuspidal Eisenstein series as a sum of intertwining periods (the name of these functionals is explained in \textit{H. Jacquet, E. Lapid} and \textit{J. Rogawski} [J. Am. Math. Soc. 12, 173--240 (1999; Zbl 1012.11044)] ). That sum of intertwining periods has a meromorphic continuation and satisfies a set of functional equations. From the main result one also deduces a relative analogue of the Maass-Selberg relations.
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 2034299
zbMATH Keywords: connected reductive group
zbMATH Keywords: cuspidal Eisenstein series
zbMATH Keywords: sum of intertwining periods
zbMATH Keywords: Maass-Selberg relations
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
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full work available at URL: s0012-7094-03-12016-5
OpenAlex ID: W2015613779
description: scientific article; zbMATH DE number 2034299