Vanishing periods of cusp forms over modular symbols
type: Item
instance of: scholarly article
title: Vanishing periods of cusp forms over modular symbols
zbMATH Open document ID: 0786.11028
DOI: 10.1007/BF01445131
author: Avner Ash
author: David Ginzburg
author: Steve Rallis
published in: Mathematische Annalen
publication date: 1994-03-23T00:00:00Z
full work available at URL: https://eudml.org/doc/165111
review text: This paper studies the integral of a cuspidal cohomology class of an arithmetic group \(\Gamma\) over a modular symbol. A modular symbol is the image modulo \(\Gamma\) of an orbit in the appropriate symmetric space of a reductive \(\mathbb{Q}\)-subgroup \(H\) of the ambient \(\mathbb{Q}\)-group \(G\). A general formula is given for this period in terms of an adelic integral of a coefficient of the cohomology class, where we view this coefficient as an automorphic function on \(G\). Using methods from the theory of automorphic functions, we prove that these periods vanish in several infinite families of cases.
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F75
zbMATH DE Number: 537279
zbMATH Keywords: vanishing of periods of cusp forms
zbMATH Keywords: period integrals
zbMATH Keywords: cuspidal cohomology
zbMATH Keywords: arithmetic group
zbMATH Keywords: modular symbol
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537279