Stabilization of periods of Eisenstein series and Bessel distributions on \(GL(3)\) relative to \(U(3)\)
type: Item
instance of: scholarly article
title: Stabilization of periods of Eisenstein series and Bessel distributions on \(GL(3)\) relative to \(U(3)\)
zbMATH Open document ID: 0983.11022
published in: Documenta Mathematica
publication date: 2000-07-23T00:00:00Z
full work available at URL: https://eudml.org/doc/121726
full work available at URL: 12.html
review text: Let \(E/F\) be a quadratic extension of number fields, let \(G = \text{Res}_{E/F} \text{GL}(3)\) and let \(H\) be the quasi-split \(\text{U}(3)\) relative to \(E/F\). In the relative trace formula for the pair \((G,H)\), distributions involving (regularized) periods of automorphic forms on \(G\) appear at the spectral side. These ``relative Bessel distributions'' are matched with ``Bessel distributions'' on \(G' = \text{GL}(3)\) in case they correspond to cuspidal representations. In the present paper, a stabilization of the relative Bessel distributions corresponding to Eisenstein series is defined, and it is proved that the stabilized distributions match with Bessel distributions on \(G'\). The stabilization is effectuated writing the regularized period of an Eisenstein series as a sum of four factorizable distributions. The local factors at the unramified places are expressed in terms of \(L\)-functions, a computation for which the authors used Mathematica.
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 1477085
zbMATH Keywords: Eisenstein series
zbMATH Keywords: relative Bessel distributions
zbMATH Keywords: stabilization
zbMATH Keywords: periods of automorphic forms
zbMATH Keywords: stability distributions
author: Erez Lapid
author: Jonathan Rogawski
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1477085