Special values of automorphic L-functions and periods

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800017
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto University (2015-2017); Kyushu University (2014)
• Principal Investigator: Yamana Shunsuke 京都大学, 白眉センター, 特定助教 (50633301)
• Project Period (FY): 2014-04-01 – 2018-03-31
• 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

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.

Free Research Field

整数論