### 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 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.

Original language | English |
---|---|

Pages (from-to) | 553-581 |

Number of pages | 29 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 51 |

Issue number | 3 |

Publication status | Published - 1999 Jul |

### Fingerprint

### Keywords

- Hermitian forms
- Local densities
- Spherical functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Spherical functions and local densities on hermitian forms.** / Hironaka, Yumiko.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 51, no. 3, pp. 553-581.

}

TY - JOUR

T1 - Spherical functions and local densities on hermitian forms

AU - Hironaka, Yumiko

PY - 1999/7

Y1 - 1999/7

N2 - 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.

AB - 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.

KW - Hermitian forms

KW - Local densities

KW - Spherical functions

UR - http://www.scopus.com/inward/record.url?scp=0012949746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012949746&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012949746

VL - 51

SP - 553

EP - 581

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 3

ER -