Open Access
July, 1999 Spherical functions and local densities on hermitian forms
J. Math. Soc. Japan 51(3): 553-581 (July, 1999). DOI: 10.2969/jmsj/05130553


First we give a formula of spherical functions on certain spherical homogeneous 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 on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.


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Yumiko HIRONAKA. "Spherical functions and local densities on hermitian forms." J. Math. Soc. Japan 51 (3) 553 - 581, July, 1999.


Published: July, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0936.11024
MathSciNet: MR1691493
Digital Object Identifier: 10.2969/jmsj/05130553

Primary: 11E95
Secondary: 11E39

Keywords: hermitian forms , Local densities , Spherical functions

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 3 • July, 1999
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