An invariant trace formula for the universal covering group of \(\text{SL}(2,\mathbb{R})\)
type: Item
instance of: scholarly article
title: An invariant trace formula for the universal covering group of \(\text{SL}(2,\mathbb{R})\)
zbMATH Open document ID: 0828.11030
DOI: 10.1007/BF02108286
author: Werner Hoffmann
published in: Annals of Global Analysis and Geometry
publication date: 1996-01-07T00:00:00Z
review text: The fundamental group of \(\text{SL} (2, \mathbb{R})\) is \(\mathbb{Z}\), so that the group possesses a universal cover which is a \(\mathbb{Z}\)-cover. The purpose of the author in this paper is to give the fullest form of the Selberg trace formula (i.e. for Hecke operators) for discrete groups of finite covolume in this universal cover. It turns out that the projection in \(\text{SL} (2, \mathbb{R})\) is again discrete and of finite covolume so that in fact one is dealing with automorphic forms of nonintegral weight for Fuchsian groups of finite covolume (see \S 3 of this paper). The author develops the representation theory and the harmonic analysis in the framework of the universal covering and applies these to prove the versions of the trace formula appropriate to this situation.
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 762849
zbMATH Keywords: universal cover
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: Hecke operators
zbMATH Keywords: discrete groups of finite covolume
zbMATH Keywords: automorphic forms of nonintegral weight
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: representation
zbMATH Keywords: harmonic analysis
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02108286
OpenAlex ID: W1975475570
description: scientific article; zbMATH DE number 762849