TY - JOUR

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

AU - Hironaka, Y.

N1 - Funding Information:
2000 Mathematics Subject Classification. Primary 11F85; Secondary 11E95, 11F70, 22E50. Key words and phrases. Spherical function, p-adic homogeneous space, prehomogeneous vector space. Partly supported by Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan.

PY - 2005

Y1 - 2005

N2 - Let dubble struck G sign be a connected reductive linear algebraic group and dubble struck X sign a dubble struck G sign-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of dubble struck G sign 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 dubble struck G sign be a connected reductive linear algebraic group and dubble struck X sign a dubble struck G sign-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of dubble struck G sign 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

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U2 - 10.1007/BF02942047

DO - 10.1007/BF02942047

M3 - Article

AN - SCOPUS:33749420654

SN - 0025-5858

VL - 75

SP - 285

EP - 311

JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

ER -