2014 Fiscal Year Final Research Report
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 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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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 |
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| 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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| Free Research Field |
整数論
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