2017 Fiscal Year Final Research Report
Study of congruences and p-adic properties for modular forms with several variables
| Project/Area Number |
26800026
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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 | Fukuoka Institute of Technology (2015-2017)
Ritsumeikan University (2014) |
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Principal Investigator |
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| Research Collaborator |
Boecherer Siegfried
KODAMA Hirotaka
TAKEMORI Sho
NAGAOKA Shoyu
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 法p特異モジュラー形式 / 合同 / p進 / Siegelモジュラー形式 / Fourier係数 / Ramanujan作用素 / テータ作用素 / Eisenstein級数 |
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| Outline of Final Research Achievements |
The reporter has been studied congruences and p-adic properties for modular forms of several variables, keeping in mind that he applies them to zeta functions (L-functions) which have many number theoretical information such as primes. In the previous study, the reporter found some examples of Siegel modular forms not satisfying the condition of several variables version of that in Serre's p-adic theory of modular forms of one variable. He named such the notions "mod p singular modular forms" and has studied it. As results of this study, he obtained some conditions which should be satisfied by the weights of mod p singular modular forms, and he also obtained the weight conditions for the "kernel of theta operator modulo p" which is a weaker version of the notion of "mod p singularity". As applications of these results, he got also some information of p-factor of special values of L-functions which appear in the Fourier coefficients of the Klingen type Eisenstein series.
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| Free Research Field |
整数論、モジュラー形式
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