### Abstract

In §1, after defining spherical functions on homogeneous spaces, we examine the case of symmetric forms as an enlightening example. In §2, we introduce a general formula of spherical functions using functional equations under suitable assumption. In §3, we study a certain mechanism of functional equations of spherical functions.

Original language | English |
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Title of host publication | NUMBER THEORY |

Editors | WENPENG ZHANG, YOSHIO TANIGAWA |

Pages | 81-95 |

Number of pages | 15 |

Publication status | Published - 2006 Dec 1 |

### Publication series

Name | Developments in Mathematics |
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Volume | 15 |

ISSN (Print) | 1389-2177 |

### Keywords

- Pre- homogeneous vector spaces
- Relative invariants
- Spherical functions
- p-adic homogeneous spaces

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Hironaka, Y. (2006). Spherical functions on p-adic homogeneous spaces. In WENPENG. ZHANG, & YOSHIO. TANIGAWA (Eds.),

*NUMBER THEORY*(pp. 81-95). (Developments in Mathematics; Vol. 15).