| Project/Area Number |
24840033
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
YAMANA Shunsuke 九州大学, 数理(科)学研究科(研究院), 助教 (50633301)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 保型表現 / L函数 / 周期 / リフティング / Eisenstein級数 / テータリフト / Gross-Prasad予想 / regularization / 保型形式 / 跡公式 / distinghuished表現 / 被覆群 |
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| Research Abstract |
I gave a necessary and sufficient condition for the nonvanishing of theta liftings. I constructed regularization of various period integrals of automorphic forms. Applications include a generalization of the theory of tensor product L-functions for general linear groups, a characterization of GL(n,F)-distinguished residual automorphic representations of GL(n,E), necessary conditions for non-vanishing of periods of Gross-Prasad type of generic automorphic representations on products of unitary groups or metaplectic groups.
Moreover, we characterize cuspidal automorphic representations of GL(6) whose exterior cube L-functions have a pole and develop a theory of a Rankin-Selberg integral representation representing the symmetric square L-function for general linear groups and characterize its pole in terms of period integrals with respect to exceptional representations of the double cover of general linear groups.
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