| Project/Area Number |
21540014
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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 | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Tamotsu 京都大学, 大学院・理学研究科, 教授 (20211716)
HIRAGA Kaoru 京都大学, 大学院・理学研究科, 講師 (10260605)
UMEDA Tooru 京都大学, 大学院・理学研究科, 准教授 (00176728)
YAMASAKI Aiichi 京都大学, 大学院・理学研究科, 准教授 (10283590)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 志村-谷山予想 / cohomology群 / L函数の特殊値 / セルバーグのゼータ函数 / 例外的零点 / 非合同部分群 / ヒルベルトモジュラー形式 / 群cohomology / 保型形式 / 周期 |
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| Research Abstract |
We formulated a generalization of the Shimura-Taniyama conjecture, which is a fundamental problem in the theory of automorphic forms. We showed that an explicit calculation of special values of the L-function attached to a Hilbert modular form is possible using the second cohomology group ; Here Hilbert modular forms are associated to a real quadratic field. We studied exceptional zeros of Selberg zeta functions in view of the noncongruence property of Fuchsian groups.
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