1999 Fiscal Year Final Research Report Summary
Studies on arithmetic automorphic forms and zeta functions
| Project/Area Number |
09440025
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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 | Kyoto Sangyo University |
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Principal Investigator |
MURASE Atsushi Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (40157772)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIDA Hisashi Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (10103714)
KATSURA Masashi Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (80065870)
MIZUHARA Akira Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (30065776)
SUGANO Takashi Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (30183841)
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| Project Period (FY) |
1997 – 1999
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| Keywords | automorphic forms / algebraic group / Fourier-Jacobi expansion / metaplectic representation / Heisenberg goup / automorphic L-function / theta lift / Howe correspondence |
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| Research Abstract |
(6) A New splitting of metaplectic representations of unitary groups and a simple proof of Howe's character formula
In this research project, we studies automorphic forms on unitary groups, in particular their arithmeticity, and related representation theory of algebraic groups over local fields. Our main results, which are joint works with T.Sugano except 6, are summarized as follows.
(1) A New simple proof and refinement of epsilon dichotomy for U(1)
(2) Adelic reformulation and refiment of the theory of Fourier-Jacobi expansion of automorphic forms on U(2,1) originally due to T.Shintani
(3) Explicit calculation of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1)
(4) A criterion for the non-vanishing of Fourier-Jacobi expansion of holomorphic Eisenstein series on U(2,1) in terms of the critical central values of Hecke L-functions
(5) Adelic reformulation of Kudla lift
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