2011 Fiscal Year Final Research Report
Study onε-factor of automorphic representations and conductor of remified components
| Project/Area Number |
21540017
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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 | Okayama University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MORIYAMA Tomonori 大阪大学, 大学院・理学研究科, 准教授 (80384171)
YASUDA Seidai 京都大学, 数理解析研究所, 助教 (90346065)
MIYAUCHI Michitaka 京都大学, 大学院・理学研究科, 研究員 (70533644)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKANO Keiji 明石工業高等専門学校, 一般教育, 准教授 (40332043)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 保型形式 / 表現論 / L-関数 |
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| Research Abstract |
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 integral presentations 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).
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