2005 Fiscal Year Final Research Report Summary
Arithmetic study of Fourier coefficients of modular forms of half integral weight and Siegel modular forms
| Project/Area Number |
16540003
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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 | SAITAMA UNIVERSITY |
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Principal Investigator |
KOJIMA Hisashi Saitama University, Faculty of science, Professor, 理学部, 教授 (90146118)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEUCHI Kisao Saitama University, Faculty of science, Professor, 理学部, 教授 (00011560)
SAKAI Fumio Saitama University, Faculty of science, Professor, 理学部, 教授 (40036596)
MIZUTANI Tadayoshi Saitama University, Faculty of science, Professor, 理学部, 教授 (20080492)
SAKAMOTO Kunio Saitama University, Faculty of science, Professor, 理学部, 教授 (70089829)
KISHIMOTO Takashi Saitama University, Faculty of science, Assistant, 理学部, 助手 (20372576)
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| Project Period (FY) |
2004 – 2005
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| Keywords | modular forms of half integral weight / zeta function / Jacobi form / modular forms / Maass wave form |
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| Research Abstract |
(1) We shall constract the Shimura correspondence S from Hilbert-Maass wave forms f of half integral weight over algebraic number field to Hilbert-Maass wave forms S(f) of integral weight over algebraic number fields. Moreover, we establish an explicit connection between the square of Fourier coefficients of f and the central value of quadratic twisted L-series associated with the image S(f) off.
(2) W.Kohnen reformulated the Ikeda lifting as a linear mapping and he formulated a Maass space of Siegel modular forms of degree 2n. Moreover, he purposed a conjecture that the image of Ikeda lifting is equal to the Maass space of degree 2n. In a joint work with W.Kohnen, we proved that this conjecture is ture in the case where 4|n and 4|n-1.
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