A p-adic approach to the special value formula of L-functions
| Project/Area Number |
25707001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University (2016-2017)
Tohoku University (2013-2015) |
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Principal Investigator |
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| Research Collaborator |
OTA Kazuto 慶応大学, 理工学部, 特任助教 (70770775)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2016: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2015: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 整数論 / L-関数 / 岩澤理論 / p進 / BSD予想 / 保型形式 / 代数学 / 数論幾何 / Gross-Zagier公式 / p進L関数 / Heegerサイクル / L-関数の特殊値 / Bloch-Kato予想 / p進L-関数 / p進高さ関数 / L関数 / 数論幾何学 / L関数の特殊値 / Heegner cycle |
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| Outline of Final Research Achievements |
We proved the p-adic Gross-Zagier formula for higher weight modular forms at non-ordinary primes. We also showed a Coates-Wiles type theorem and a one-side divisibility of Iwasawa main conjecture for Galois representations of modular forms twisted by anticyclotomic Hecke characters. This research is closely related to the Birch and Swinnerton-Dyer conjecture and gives an important example of the Beilinson-Bloch-Kato conjecture, which is a central theme of the modern number theory containing the Birch and Swinnerton-Dyer conjecture as a special case.
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Report
(6 results)
Research Products
(21 results)
