Theta correspondence for Eisenstein series
type: Item
instance of: scholarly article
title: Theta correspondence for Eisenstein series
zbMATH Open document ID: 0773.11028
DOI: 10.1007/BF02571525
published in: Mathematische Zeitschrift
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/174316
review text: The authors study the theta correspondence between automorphic forms on the symplectic and the split orthogonal group. Their main interest is the lifting of Eisenstein series between these groups. Since the usual integral against a theta kernel does not converge in this case they have to apply a suitable differential operator to it to make the integral converge. The results allow to connect the (Klingen-) Eisenstein series on the symplectic group formed with respect to the different maximal parabolic subgroups with the standard Eisenstein series on the split orthogonal group of varying size (and vice versa). This gives new proofs of functional equation and analytic continuation as well as information about poles and residues and a Kronecker limit formula for the Eisenstein series on the orthogonal group.
reviewed by: Rainer Schulze-Pillot
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 59947
zbMATH Keywords: automorphic forms
zbMATH Keywords: theta correspondence
zbMATH Keywords: orthogonal group
zbMATH Keywords: lifting of Eisenstein series
zbMATH Keywords: symplectic group
zbMATH Keywords: functional equation
zbMATH Keywords: analytic continuation
zbMATH Keywords: poles
zbMATH Keywords: residues
zbMATH Keywords: Kronecker limit formula
author: Anton Deitmar
author: Aloys Krieg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 59947