A computation of the gamma matrix of a family of \(p\)-adic zeta integrals
type: Item
instance of: scholarly article
title: A computation of the gamma matrix of a family of \(p\)-adic zeta integrals
zbMATH Open document ID: 0862.14015
author: W. Jay jun. Sweet
published in: Journal of Number Theory
publication date: 1996-03-18T00:00:00Z
review text: The purpose of this paper is to compute the \(\gamma\)-matrices which occur in the functional equation for the \(p\)-adic zeta integral on the space of \(n\times n\) symmetric matrices over a non-archimedean field of characteristic 0. It is a typical and important example of the computation of \(\gamma\)-matrices associated with regular prehomogeneous vector spaces. The authors also gives some applications to computing the points of reducibility of certain families of degenerate principal series representations of classical groups, to the study of Eisenstein series on these same groups and to non-vanishing of theta lifts.
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 11S40
zbMATH DE Number: 844633
zbMATH Keywords: symmetric matrix space
zbMATH Keywords: zeta integral
zbMATH Keywords: non-archimedean field
zbMATH Keywords: prehomogeneous vector spaces
zbMATH Keywords: theta lifts
reviewed by: Masakazu Muro
MaRDI profile type: Publication
full work available at URL: jnth.1995.1139
OpenAlex ID: W2056312134
DOI: 10.1006/JNTH.1995.1139
description: scientific article; zbMATH DE number 844633