### Abstract

Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G acts with open orbit. We are interested in spherical functions on X =X(k). In the present papaer, we give a unified method to obtain functional equations of spherical functions on X under the condition (AF) in the introduction, and explain functional equations are reduced to those of p-adic local zeta functions of small prehomogeneous vector spaces of limited type.

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

Pages (from-to) | 285-311 |

Number of pages | 27 |

Journal | Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2005 Dec |

### Fingerprint

### Keywords

- p-adic homogeneous space
- prehomogeneous vector space
- Spherical function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Functional equations of spherical functions on p-adic homogeneous spaces.** / Hironaka, Yumiko.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Functional equations of spherical functions on p-adic homogeneous spaces

AU - Hironaka, Yumiko

PY - 2005/12

Y1 - 2005/12

N2 - Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G acts with open orbit. We are interested in spherical functions on X =X(k). In the present papaer, we give a unified method to obtain functional equations of spherical functions on X under the condition (AF) in the introduction, and explain functional equations are reduced to those of p-adic local zeta functions of small prehomogeneous vector spaces of limited type.

AB - Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G acts with open orbit. We are interested in spherical functions on X =X(k). In the present papaer, we give a unified method to obtain functional equations of spherical functions on X under the condition (AF) in the introduction, and explain functional equations are reduced to those of p-adic local zeta functions of small prehomogeneous vector spaces of limited type.

KW - p-adic homogeneous space

KW - prehomogeneous vector space

KW - Spherical function

UR - http://www.scopus.com/inward/record.url?scp=33749420654&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749420654&partnerID=8YFLogxK

U2 - 10.1007/BF02942047

DO - 10.1007/BF02942047

M3 - Article

AN - SCOPUS:33749420654

VL - 75

SP - 285

EP - 311

JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

SN - 0025-5858

IS - 1

ER -