2011 Fiscal Year Final Research Report
Spherical functions on p-adic homogeneous spaces and those applications
| Project/Area Number |
20540029
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Waseda University |
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Principal Investigator |
HIRONAKA Yumiko 早稲田大学, 教育・総合科学学術院, 教授 (10153652)
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| Co-Investigator(Renkei-kenkyūsha) |
SATO Fumihiro 立教大学, 理学部, 教授 (20120884)
KAMANO Ken 大阪工業大学, 工学部, 特任講師 (50409611)
OKAMOTO Akihiko 早稲田大学, 教育総合科学学術院, 助手 (50608825)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 数論 |
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| Research Abstract |
We intend to investigated certain$ p$-adic homogeneous spaces together with spherical functions and have number theoretic applications. We have approached this purpose in the following way : 1) to formulate expression formulas of spherical functions which can be widely applied ; 2) to formulate explicit formulas of spherical functions for concrete examples and analyze the spaces ; 3) to obtain number theoretic interesting quantities for the spaces of symmetric forms and hermitian forms.
The most important result is to complete the theory of spherical functions on the space of unramified unitary hermitian matrices.
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