Perrods and cogruences of modular forms
| Project/Area Number |
24540005
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
KATSURADA Hidenori 室蘭工業大学, 工学(系)研究科(研究院), 教授 (80133792)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | congruence / lift / L-values / Koecher-Maass series / Gross-Keating invariant / Siegel series / Hermitian Ikeda lift / Kima-Shahidi lift / period congruence / 周期 / 合同 / ジーゲル保型形式 / 特殊値 |
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| Outline of Final Research Achievements |
We proposed conjectures on prime ideals giving congruence between various lifts (eg. Ikeda-Miyawaki lift, Kim-Shahidi lift) and modular forms not coming from the lifts. I also gave numerical examples which support the conjectures. (Joint works with T. Ibukiyama, C. Poor, D. Yuen and S. Takemori) I gave an explicit formula for the twisted Koecher-Maass series of the Duke-Imamoglu-Ikeda lift.We also applied this to special values of the Rankin-Selberg series of half-integral weight modular form.
I investigated the properties of the Gross-Keating invariants of quadratic forms, and as an application we gave an explicit formula of the Siegel series of a quadartic forms over any non-archimedian local field.
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Report
(4 results)
Research Products
(16 results)
