2013 Fiscal Year Final Research Report
Periods of automorphic forms and harmonic analysis
| Project/Area Number |
22740021
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
ICHINO Atsushi 京都大学, 理学(系)研究科(研究院), 准教授 (40347480)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 保型形式 / 周期 / 形式次数 / テータ対応 |
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| Research Abstract |
In this research, we have studied the global (Gan-)Gross-Prasad conjecture on the relation between periods of automorphic forms on special orthogonal and unitary groups and special values of automorphic L-functions. In particular, toward an application to relative trace formulas, we extended a theory of regularized periods which are not necessarily convergent to those appearing in the (Gan-)Gross-Prasad conjecture.
Also, as a local analogue of periods of automorphic forms, we have studied the relation between the harmonic analysis on reductive groups over local fields and arithmetic invariants. In particular, we proved that the formal degree conjecture, which relates the formal degrees of square-integrable representations with special values of adjoint gamma-factors, is compatible with the functorial lift defined by the local theta correspondence.
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