On Fourier coefficients of automorphic forms of symplectic groups
type: Item
instance of: scholarly article
title: On Fourier coefficients of automorphic forms of symplectic groups
zbMATH Open document ID: 1027.11034
author: Steve Rallis
author: David Soudry
author: David Ginzburg
published in: Manuscripta Mathematica
publication date: 2003-07-02T00:00:00Z
review text: For a number of reasons it is interesting to determine Fourier coefficients of automorphic forms. The best known Fourier coefficient is the so-called Whittaker Fourier coefficient. While every cuspidal representation of \(\text{GL}_n(\mathbb A)\) has such a Fourier coefficient, for other classical groups this is not true. In the paper under the review, the authors study Fourier coefficients of cuspidal representations on symplectic groups. They associate to each unipotent orbit a set of Fourier coefficients of an automorphic form on \(\text{Sp}_{2n}\) or its double cover. They prove that every cuspidal representation on a symplectic group has a non-trivial Fourier coefficient with respect to a certain type of unipotent class.
reviewed by: Marko Tadić
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E55
zbMATH DE Number: 1945292
zbMATH Keywords: automorphic representations
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: unipotent orbits
zbMATH Keywords: symplectic groups
zbMATH Keywords: adele rings
MaRDI profile type: Publication
full work available at URL: s00229-003-0355-7
OpenAlex ID: W1987814262
DOI: 10.1007/S00229-003-0355-7
description: scientific article; zbMATH DE number 1945292