Abstract
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 of nondegenerate unramified hermitian forms on a -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 , and parametrize of all spherical functions on . Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.
Citation
Yumiko HIRONAKA. "Spherical functions and local densities on hermitian forms." J. Math. Soc. Japan 51 (3) 553 - 581, July, 1999. https://doi.org/10.2969/jmsj/05130553
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