1998 Fiscal Year Final Research Report Summary
Automorphic forms and L functions on algebraic groups
| Project/Area Number |
09640040
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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 | Kanazawa University |
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Principal Investigator |
SUGANO Takashi Fac.of Sci., Kanazawa University Professor, 理学部, 教授 (30183841)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIOKA Atsushi Fac.of Sci., Kanazawa University Assistant, 理学部, 助手 (30293335)
HAYAKAWA Takayuki Fac.of Sci., Kanazawa University Assistant, 理学部, 助手 (20198823)
MORISHITA Masanori Fac.of Sci., Kanazawa University Associate Professor, 理学部, 助教授 (40242515)
YAMADA Mieko Fac.of Sci., Kanazawa University Professor, 理学部, 教授 (70130226)
ITO Tatsuro Fac.of Sci., Kanazawa University Professor, 理学部, 教授 (90015909)
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| Project Period (FY) |
1997 – 1998
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| Keywords | automorphic form / L function / Shintani function / Weil representation / theta function |
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| Research Abstract |
1. Automorphic L-functions on unitary groups (joint work with A.Murase)
We poved the analytic continuation and the functional equations of the standard L-function associated with a holomorphic cusp form on a unitary group. The key ingredient in the proof is a study of Shintani functions.
2. Automorphic forms on unitary groups of degree 3 and primitive theta functions (joint work with A.Murase)
For the study of arithmetical automorphic forms on a unitary group of degree 3, primitive theta functions are fundamental. We investigated a metaplectic representation of U(1) acting on the space of local primitive theta functions and gave its explicit irreducible decomposition.
As an application, we determined the refined Fourier-Jacobi expansion of holomorphic Eisenstein series.
3. theta lift and Jacobi group (joint work with A.Murase)
Since Kudla lift is a restriction of Oda lift, we can construct automorphic forms on unitary groups of degree 3 from Jacobi forms explicitly. We gave another formulation of refined Fourier-Jacobi expansion of holomorphic Eisenstein series using Jacobi type Eisenstein series.
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