Arithmetic of automorphic forms, an extension of its researching field in terms of explicit constructions
| Project/Area Number |
24540025
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kumamoto University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 5次元双曲空間 / マース保型形式 / リフティング / ラマヌジャン予想 / 保型L関数の中心値 / 超幾何関数 / 例外型リー群 / マースカスプ形式 / ５次元双曲空間 / Ramanujan予想 / 一般化ホウィッタカー関数 / Rankin L関数 / 超幾何級数 / テータリフト |
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| Outline of Final Research Achievements |
The theory of automorphic forms, which is my reserach object, has been playing a crucial role in the number theroy as the achievements of the Langlands program indicate. The aim of this research is to deepen researches on automorphic forms in terms of their explicit construction. I have obtained two results: One is to provide explicit construction of automorphic forms which are counterexamples of the Ramanujan conjecture, and another one is a result on the non-vanishing of the central values of some automorphic L-functions in terms of special values of certain hypergeometric functions, whose origin does not come from the number theory.
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Report
(4 results)
Research Products
(10 results)
