2017 Fiscal Year Final Research Report
Pursuing the dream of trinity of complex and real multiplications and the moonshine of the j-function by its novel extension
| Project/Area Number |
15K13428
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | j-関数 / 実二次体 / 虚数乗法 / モジュラー微分方程式 / モックモジュラー形式 |
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| Outline of Final Research Achievements |
We revisited the classification of two dimensional conformal field theory by using a modular differential equation which was formerly studied with Zagier, and by generalizing that, we showed the non-exsistence of a certain rational vertex operator algebra. Also, by looking at the higher order cases, we showed the theory can be applicable to a classification of vertex operator algebras. Together with Mizuno, we established a formula describing class numbers of imaginary quadratic fields in terms of continued fraction expansions of real quadratic numbers, by computing the L-function of general quadratic genus characters. This gives a counterpart in the case of primes congruent to 1 modulo 4 of the theorem of Hirzebruch-Zagier.
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| Free Research Field |
数論
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