Differential equations satisfied by modular forms
| Project/Area Number |
17K14213
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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 |
Basic analysis
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| Research Institution | Niihama National College of Technology |
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Principal Investigator |
Matsuda Kazuhide 新居浜工業高等専門学校, 数理科, 准教授 (20550106)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
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| Keywords | モジュラー形式 / テータ関数 / 有理指標 / Ramanujan の微分方程式 / cubic theta 関数 / Ramanujan の方程式 / 微分体 / Jacobi の微分公式 |
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| Outline of Final Research Achievements |
We concretely construct examples of differential equations satisfied by modular forms. In particular, we treat modular forms of levels 3-6. We obtain applications to quadratic forms. Moreover, we discover high level versions of Jacobi's derivative formula and Jacobi's quartic identity.
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| Academic Significance and Societal Importance of the Research Achievements |
モジュラー形式が満たす微分方程式は、これまで可積分系および整数論の両分野から研究されてきた。本研究により新たな例が得られたことにより、両分野の新たな発展が期待できる。
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Report
(5 results)
Research Products
(4 results)
