Periods and congruence of modular forms, and Selmer group
| Project/Area Number |
21540004
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Muroran Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 数論 / 合同 / Triple L関数 / Ikeda-Miyawaki lift / Poincare級数 / twisted Kocher-Maass級数 / Rankin-Selberg級数 / 1次従属性 / スタンダードL関数 / Ikeda lift / 保型形式の合同 / Kim-Shahidi lift / エルミートモジュラー形式 / Rankin-Selberg zeta関数 / Ikeda予想 / スタンダードゼータ関数 / Harder予想 / Bloch-Kato予想 |
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| Research Abstract |
(1) We solved Ikeda's conjecture on the period of the Hermitian Ikeda lift.
(2) We compute the special values of ceratain vector valued Siegel modular forms and confirmed a conjecture proposed by N. Dummigan (joint work with N. Dummigan and T. Ibukiyama). Moreover we computed the special values of the standard L-function of the Kim-Shahidi lift of Ramanujan delta function △, and confirmed that it is complatible with Zagier's conjecture on the special values of symmetric forth L function of △(joint work with T. Ibukiyama).
(3) We established an algorithm for computing the special values of the triple L function of elliptic modular forms (joint work with T. Ibukiyama). By using it we considered the congruence between Ikeda-Miyawaki lift and non- Ikeda-Miyawaki lift (joint work with T. Ibukiyama, C. Poor, and D. Yuen).
(4) We gave an explicit formula for the Fourier coefficient of the Poincare series for the congruence subgroup Γ_0 (N) of S_<p2>(Z).
(5) We gave an explicit formula of twisted Koecher-Maass series of the Saito-Kurokawa lift. As an application we obtained a linear dependence of the special values of the Rankin-Selberg series of certain half-integral weight modular forms (joint work with Y. Mizuno). Moreover we gave an explicit formula of twisted Koecher-Maass series of the Duke-Imamoglu-Ikeda lift.
(6) We consider congruence between the Klingen-Eisenstein series and cups forms (joint work with S. Mizumoto).
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Report
(4 results)
Research Products
(32 results)
