Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\)
type: Item
instance of: scholarly article
title: Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\)
zbMATH Open document ID: 1158.22014
author: Tadashi Miyazaki
published in: Manuscripta Mathematica
publication date: 2009-02-26T00:00:00Z
review text: In the theory of automorphic forms, Whittaker functions (WF) are a generalization of Fourier coefficients of cuspidal modular forms. They provide important analytical tools for the study of automorphic \(L\)-functions. In the present paper WF for principal series representations of \(\text{SL}_3({\mathbb R})\) are studied. This restricted choice allows for quite explicit formulae. The latter are given for radial parts of certain WF. A set of differential equations of Lie-theoretic origin is determined, that are satisfied by WF. Formal power series solutions to these differential equations are studied. Finally, an integral representation of some WF is given.
reviewed by: Anton Deitmar
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 5520096
MaRDI profile type: Publication
full work available at URL: s00229-008-0209-4
OpenAlex ID: W1996312839
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DOI: 10.1007/S00229-008-0209-4
description: scientific article; zbMATH DE number 5520096