Study on p-adic L-functions and p-adic periods for modular forms
Project/Area Number |
23740015
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | 岩澤理論 / p進L関数 / 保型形式 / Beilinson予想 / Rankin-Selberg L関数 / regulator写像 / Beilinson-Flach元 / 久賀-佐藤多様体 / 国際研究者交流(フランス) / 岩澤主予想 / 志村曲線 / CM点 / Euler system / 肥田理論 / 保型L関数 / p進周期 / 岩澤不変量 |
Outline of Final Research Achievements |
In this research, we investigated properties of special values of (p-adic) L-functions and (p-adic) periods associated to elliptic modular forms. Moreover we studied Iwasawa main conjecture and Beilinson conjecture. In joint work with M.-L. Hsieh, we constructed anticyclotomic p-adic L-functions for elliptic modular forms and showed one-sided divisibility of anticyclotomic Iwasawa main conjecture under mild assumptions. Through joint research with F. Brunault, we also showed a weak version of Beilinson conjecture for Rankin-Selberg products of elliptic modular forms. Furthermore, in joint work with Satoshi Kondo and Takuya Yamauchi, we studied algebraic K-group of curves of GL(2)-type over function fields and proved a result on surjectivity of boundary maps.
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Report
(5 results)
Research Products
(32 results)