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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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / ムーンシャイン / トンプソン級数 |
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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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Report
(4 results)
Research Products
(29 results)
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[Presentation] Finite multiple zeta values2016
Author(s)
Masanobu Kaneko
Organizer
Diophantine Analysis and Related Topics
Place of Presentation
School of Mathematics and Statistics Wuhan University, China
Year and Date
2016-03-10
Related Report
Int'l Joint Research / Invited
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[Presentation] 有限多重ゼータ値2015
Author(s)
Masanobu Kaneko
Organizer
京都大学数学談話会
Place of Presentation
京都大学数理解析研究所
Year and Date
2015-12-09
Related Report
Invited
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[Presentation] On finite multiple zeta values2015
Author(s)
Masanobu Kaneko
Organizer
Seminaire de Theorie des Nombres de Caen
Place of Presentation
Laboratoire de Mathematiques,Universite de Caen, France
Year and Date
2015-09-04
Related Report
Int'l Joint Research / Invited
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[Presentation] On finite multiple zeta values2015
Author(s)
Masanobu Kaneko
Organizer
Seminaire de Groupe d’Etude sur les Problemes Diophantiens
Place of Presentation
Universite Paris 6 Pierre et Marie Curie-Jussieu, France
Year and Date
2015-09-03
Related Report
Int'l Joint Research / Invited
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[Presentation] On the elliptic modular function j2015
Author(s)
Masanobu Kaneko
Organizer
Seminar on Algebra, Geometry and Physics
Place of Presentation
Max Planck Institute for Mathematics, Germany
Year and Date
2015-08-11
Related Report
Int'l Joint Research / Invited
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