2022 Fiscal Year Final Research Report
Periods, congruence and special values of L functions for modular forms
| Project/Area Number |
16H03919
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University (2020, 2022)
Muroran Institute of Technology (2016-2019) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | Hermitian Ikeda lift / Kim-Yamauchi lift / period relation / Gross-Keating invariant / Siegel series / Harder conjecture |
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| Outline of Final Research Achievements |
1.We proved an adelic version of Ikeda's conjecture on the period of the Hermitian Ikeda lift. 2.We proposed a conjecture on the period of the Kim-Yamauchi lift, and proved it(joint work with H.H. Kim and T.Yamauchi). 3.We constructed a fundamental
theory of quadratic forms over non-archimedean local fields, and gave an explicit formula for the Siegel series of a quadratic form (joint work with T. Ikeda). 4.We reformulated Harder's conjecture, and proved it for some cases (joint work with H. Atobe, M. Chida, T.Ibukiyama and T.Yamauchi).
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| Free Research Field |
整数論
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| Academic Significance and Societal Importance of the Research Achievements |
(1) ユニタリー群やE7型例外群の保型形式に関して重要な興味深い結果を与えるとともに，例外型Jordan代数の局所理論に新たな知見を加えた．(2) 局所体の2次形式の理論をdyadic, non-dyadicに限らず統一的に扱えるようになった．また，Siegel級数の明示的な公式はDuke-Imamoglu-Ikeda liftのフーリエ係数の評価やShimura多様体のサイクルの交差数に関するKudla programにも使われ，今後も大域的な応用が見込まれる．(3) Harder予想の新しい定式化はBergstroem-Farber-van-der-Geer予想等にも新たな知見を与える．
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