Spherical functions and local densities on hermitian forms

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Abstract

First we give a formula of spherical functions on certain spherical homo-geneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a p-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions onX. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.

Original languageEnglish
Pages (from-to)553-581
Number of pages29
JournalJournal of the Mathematical Society of Japan
Volume51
Issue number3
DOIs
Publication statusPublished - 1999 Jan 1

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Keywords

  • Hermitian forms
  • Local densities
  • Spherical functions

ASJC Scopus subject areas

  • Mathematics(all)

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