2014 Fiscal Year Final Research Report
On the relation between L-functions and periods, and the related problems in number theory
| Project/Area Number |
23740034
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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 | Tokyo University of Science |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | L関数 / 周期 / ｐ進L関数 / ｐ進周期 / スターク予想 / グロス予想 / ガンマ関数 / ｐ進ガンマ関数 |
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| Outline of Final Research Achievements |
The Artin L-functions are meromorphic functions associated with Galois representations of number fields. Stark's conjecture states an explicit formula for the leading terms of the Taylor expansions of the Artin L-functions.
The purpose of my research is to study Stark's conjecture by a new method. That is, by using Stark units, CM-periods, the multiple gamma function, and their p-adic analogues simultaneously, we tried to solve this problem. Each of them, or, the relation between two of them has been studied well so far. Recently, we provided an alternative proof of Stark's conjecture when the base field is the rational number field. Moreover we obtained some partial results concerning its generalization and submitted some papers.
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| Free Research Field |
整数論
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