2007 Fiscal Year Final Research Report Summary
Research on special values on L-functions of automorphic forms
| Project/Area Number |
17540003
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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 | Muroran Institute of Technology |
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Principal Investigator |
KATSURADA Hidenori Muroran Institute of Technology, 室蘭工業大学・工学部, Professor (80133792)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEGAHARA Yugen Muroran Institute of Technology, 工学部, Professor (10211351)
HASEGAWA Yuji Muroran Institute of Technology, 工学部, Associate Professor (30287982)
CHIGIRA Naoki Muroran Institute of Technology, 工学部, Associate Professor (40292073)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Standard zeta function / Ikeda lift / Congruenc of Siegel modular forms / Fourier-Jacobi coefficient / Rankin-elberg zeta function / Bloch-Kato conjecture / Harder's conjeture / Ikeda' conjecture |
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| Research Abstract |
(1) We gave an explicit formula for a certain Dirichlet series of Rankin-Selberg type associated with the Fourier-Jacobi coefficients of the Ikeda lifting. (Joint work with. Kawamura (Hokkaido Univ.))
(2) By using (1), we rewrote a conjecture concerning the period of the Ikeda lift proposed by T Ikeda in terms of the period of a certain half-integral weight Siegel modular forms. As a result we proved Ikeda's conjecture. (Joint work with. Kawamura (Hokkaido Univ.))
(3) We proposed a conjecture, which related the congruence between the Ikeda lift of an elliptic modular from f and non-Ikeda lift with the special values of L-functions of f. By using (2) we proved our conjecture.
(4) We gave a talk about (1), (2) and (3), for examples, on the following meetings ^*RI MS conference (2007,1.16), ^*The 52th Algebra Symposium (2007,8.7), ^*Special lecture at the annual meetings of M. S. J (2008,3.24)
(5) We gave an exact values of the standard L-function of a certain vector valued Siegel modular forms, which is related with Harder's conjecture. (Joint work with T. Ibukiyama (Osaka Unuv.).
(6) We investigate the non-vanishing of the central critical values of standard L-function of Siegel modular forms of degree 2 (Joint work with K. Matsumoto (Nagoya Univ.) and M. Chida (Tohoku Univ.))
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Research Products
(51 results)
