Products of theta series and spectral analysis
type: Item
instance of: scholarly article
title: Products of theta series and spectral analysis
zbMATH Open document ID: 0805.11039
author: Yuval Z. Flicker
author: J. G. M. Mars
published in: Journal of Number Theory
publication date: 1995-02-05T00:00:00Z
review text: The authors give a characterization of the set of cuspidal automorphic forms on PGL(2) which arise as theta lifts from a Größencharakter of a quadratic extension of the ground field. The condition is of the form \(\int \varphi (g) \Theta (g) \overline \Theta^ \chi (g)\) \(dg\) where \(\Theta\) and \(\Theta^ \chi\) are one-dimensional theta functions and \(\varphi\) is the automorphic form in question. The proof uses the decomposition of the regular representation into irreducible representations and arguments rather akin to those used in the theory of the treatment of the trace formula but which bring in the Weil representation in an essential way. The authors expect that this method will be applicable in a wide number of cases.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F72
zbMATH DE Number: 584041
zbMATH Keywords: cuspidal automorphic forms
zbMATH Keywords: theta lifts
zbMATH Keywords: grössencharacter
zbMATH Keywords: theta functions
zbMATH Keywords: Weil representation
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
full work available at URL: jnth.1994.1035
OpenAlex ID: W1969897937
DOI: 10.1006/JNTH.1994.1035
description: scientific article; zbMATH DE number 584041