2016 Fiscal Year Final Research Report
On special values of automorphic L-functions
| Project/Area Number |
25400020
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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 | Osaka City University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 保型L函数 / L函数の特殊値 / テータ対応 |
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| Outline of Final Research Achievements |
In a joint work with Kazuki Morimoto of Kobe University, we proved one direction of the Gross-Prasad conjecture in the case of special Bessel periods for SO(2n+1). Namely we proved that the non-vanishing of the special Bessel period for SO(2n+1) implies the non-vanishing of the central value of the corresponding L-function. We also proved the converse in some cases.
In another joint work with Kazuki Morimoto, we proved the algebraicity of some critical values of the tensor product L-functions for SO(V) times GL(2) where V is anisotropic. Our result involves some unbalanced cases of the Rankin triple L-function for GL(2).
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| Free Research Field |
保型L函数
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