Ramified components of automorphic representations: local theory and its application to special L-values
| Project/Area Number |
24540021
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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 | Okayama University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
YASUDA Seidai 大阪大学, 理学研究科, 准教授 (90346065)
TAKANO Keiji 明石工業高等専門学校, 一般科目, 准教授 (40332043)
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| Co-Investigator(Renkei-kenkyūsha) |
MIYAUCHI Michitaka 大阪府立大学, 高等教育推進機構, 教育拠点形成教員 (70533644)
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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 |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 保型形式 / 表現論 / ε-因子 / H-周期 / Ｈ-周期 |
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| Outline of Final Research Achievements |
Number theory investigation usually involves quite vast area of deep mathematics, like as the Fermat Last Theolem does. The Langlands Program, which led to the settlement of FLT, has been the central strategy of arithmetic since 70s. We follow the LP to study the ramification theory of the group U(3) representations in view point of L-/ε-factors. Our approach is resorting to integralpresentations of L-function of automorphic forms, whose ramified factors give us arithmetic info. The point is to find nice Whittaker functions appearing in the ramified factor. We can successfully detect where/which the nice ones are in the case of Real/unramified U(3). As an application to the global problem, we got algebraicity result for all the critical values of twisted L-function of generic cuspidal representaions on U(3).
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Report
(4 results)
Research Products
(25 results)
