Automorphic representations and special values of L-functions
| Project/Area Number |
26800021
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kobe University (2016-2017)
Kyoto University (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 保型表現 / L函数 / 保型形式の周期 / 数論 / 代数学 / 保型L函数 / p進簡約群の表現 |
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| Outline of Final Research Achievements |
We studied a relationship between special values of automorphic L-functions and periods of automorphic forms. Under certain assumptions, we proved an explicit formula of Whittaker periods for even unitary group, which is a conjecture by Lapid and Mao. Using a certain local identity which played an important role in the proof of this explicit formula, we proved formal degree conjecture in this case.
Further, in a joint work with Masaaki Furusawa (Osaka City University), we proved an explicit formula relating special Bessel periods and central values of automorphic L-functions associated to Siegel modular forms.
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Report
(5 results)
Research Products
(20 results)
