### 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 language | English |
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Pages (from-to) | 553-581 |

Number of pages | 29 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 51 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

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### Keywords

- Hermitian forms
- Local densities
- Spherical functions

### ASJC Scopus subject areas

- Mathematics(all)