On arithmetic theory of automorphic forms and special values of automorphic L-functions
| Project/Area Number |
10640028
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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 | Osaka City University (1999)
Hiroshima University (1998) |
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Principal Investigator |
FURUSAWA Masaaki Osaka City University, Faculty of Science Professor, 理学部, 教授 (50294525)
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| Co-Investigator(Kenkyū-buntansha) |
KOMORI Youhei Osaka City University, Faculty of Science Lecturer, 理学部, 講師 (70264794)
IMAYOSHI Yoichi Osaka City University, Faculty of Science Professor, 理学部, 教授 (30091656)
KAMAE Tetsuro Osaka City University, Faculty of Science Professor, 理学部, 教授 (80047258)
MATSUMOTO Keiji Hokkaido University, Graduate School of Science Assistant Professor, 大学院・理学研究科, 助教授 (30229546)
MOCHIZUKI Takuro Osaka City University, Faculty of Science Assistant, 理学部, 助手 (10315971)
都築 暢夫 広島大学, 理学部, 助手 (10253048)
木村 俊一 広島大学, 理学部, 講師 (10284150)
谷崎 俊之 広島大学, 理学部, 教授 (70142916)
隅広 秀康 広島大学, 理学部, 教授 (60068129)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1998: ¥2,500,000 (Direct Cost: ¥2,500,000)
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| Keywords | Siegel modular form / automorphic L-function / special value of L-function / Deligne's conjecture / relative trace formula / trace formula / ジーゲル保型形式 / 保型形式の持ち上げ / クルスターマン和 |
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| Research Abstract |
We proved the fundamental lemma for the unit element in the Hecke algebra for two relative trace formulas for GSp(4). Our ultimate goal is to prove Bocherer's conjecture on the central critical values of the quadratic twists of the spinor L-functions associated to holomorphic Siegel eigen cusp forms of degree two. The announcements of the fundamental lemma have been published in C. R. Acad. Sci. Paris and the details of the proof will appear elsewhere.
In the course of the proof of the fundamental lemma, we evaluated certain matrix argument Kloosterman sums explicitly in terms of the classical GL(2) Kloosterman sums. We remark that our Kloosterman sum is a special case of the generalized Kloosterman sum which appears in the Fourier coefficients of the Poincare series for the Siegel modular group. Our result on the Kloosterman sum may be of some independent interest, since it is rare that such generalized Kloosterman is evaluated explicitly.
Our second conjectural trace formula is related to the quadratic base charge for GSp (4). Our result suggests that the Jacquet-Ye criterion for the quadratic base change for GL(2) generalizes to GSp(4). This clearly deserves some further investigation. Finally our result implies that it is important to study the whole L-packet when we study the special values of automorphic L-functions. It seems very interesting to clarify the relationship between the period part of the special value expected by our result and Deligne's conjecture.
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Report
(3 results)
Research Products
(11 results)
