Differential equations satisfied by modular forms

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K14213
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Niihama National College of Technology
• Principal Investigator: Matsuda Kazuhide 新居浜工業高等専門学校, 数理科, 准教授 (20550106)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: モジュラー形式 / テータ関数 / 有理指標

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.

Free Research Field

整数論、可積分系

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。