2016 Fiscal Year Final Research Report
Iwasawa main conjecture and congruences between automorphic representations
| Project/Area Number |
15H06634
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Keywords | 数論 / L関数 / 保型表現 / 岩澤理論 |
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| Outline of Final Research Achievements |
We studied Theta functions (Yoshida lifts, Harris-Soudry-Taylor (HST) lifts) and special values of L-functions. By using an explicit inner product formula, which was obtained in our previous research, we showed that a non-vanishing result of special values of twisted Rankin-Selberg type L-functions which is associated with Hilbert modular forms over real quadratic fields under some assumptions.
We also studied an explicit relation Bessel periods and special values of L-functions, which is a generalization of our previous result. An explicit result is not yet available, however, we find a formulation which is an analogue of Yoshida lifts case.
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| Free Research Field |
数論
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