Special values of automorphic L-functions and periods
| Project/Area Number |
26800017
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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 | Kyoto University (2015-2017)
Kyushu University (2014) |
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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 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | L関数 / ヒルベルトモジュラー形式 / ジーゲルモジュラー形式 / 周期 / 池田リフティング / アイゼンシュタイン級数 / 格別表現 / テータ対応 / p進L関数 / j関数 / 志村多様体 / Boecherer予想 / リフティング / モジュライスタック / テータリフト / 退化主系列表現 / 交点数 / 池田リフト / 斎藤-黒川リフト / Kudlaリフト / Arthur予想 / ヒルベルト保型形式 / ジーゲル保型形式 / エルミート保型形式 / ジーゲル級数 / 志村対応 / ジャッケ積分 / 二次対称積L関数 / 二次対称積L因子 / Rankin-Selberg法 / 例外表現 / 二重被覆群 / 三重積周期 / Whittaker模型 |
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| Outline of Final Research Achievements |
I developed a local theory of twisted symmetric square L-factors of representations of general linear groups and characterized its pole in terms of distinction by exceptional representations. I constructed Hilbert-Siegel cusp forms and Hilbert-Hermite cusp forms explicitly by generalizing Ikeda's construction of a lifting of elliptic cusp forms to a lifting of Hilbert cusp forms, and applied it to the basis problem and the theory of quadratic forms.
I constructed anti-cyclotomic p-adic spinor L-functions of paramodular Siegel cusp forms of degree 2 by using the Bessel period.
I computed Fourier coefficients of the non-central derivative of degree 4 Siegel Eisenstein series and relate it to the central derivative of degree 3 Siegel Eisenstein series.
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Report
(5 results)
Research Products
(68 results)
