1998 Fiscal Year Final Research Report Summary
Automorphic forms of several variables and spherical functions of homoge-neous spaces
| Project/Area Number |
09440016
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
YAMAZAKI Tadashi Kobe University Faculty of Science Professor, 理学部, 教授 (30011696)
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| Co-Investigator(Kenkyū-buntansha) |
MURASE Atsushi Kyoto Sangyo University Faculty of Science Professor, 理学部, 教授 (40157772)
SUGANO Takashi Kanazawa University Faculty of Science Professor, 理学部, 教授 (30183841)
SEKIGUCHI Hideko Kobe University Faculty of Science, 理学部, 助手 (50281134)
TAKAYAMA Nobuki Kobe University Faculty of Science Professor, 理学部, 教授 (30188099)
SAITO Masahiko Kobe University Faculty of Science Professor, 理学部, 教授 (80183044)
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| Project Period (FY) |
1997 – 1998
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| Keywords | automorphic form / Hecke algebra / spherical function |
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| Research Abstract |
The spherical function or the Shintani function of homogeneous spaces are important in order to study the Fourier expansion of period of automorphic forms and L-functions associated to automorphic forms.
We studied mainly the Shintani function of the classical groups. in particular we proved uniqueness and existence of the Shintani function and in some cases we obtained explicit formulas for them. We applied them to examine analytic and arithmetic properties of automorphic L-functions. (Muarase-Sugano)
It would be our next objective to define suitable geometrical objects associated to spherical subgroups and to interpret the Shintani function in terms of their cohomology groups.
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