Modular Ordinary Differential Equations on SL(2, ℤ) of Third Order and Applications

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Authors: Chen, Zhijie, Lin, Chang-Shou, Yang, Yifan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211532
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Modular Ordinary Differential Equations on SL(2, ℤ) of Third Order and Applications. Zhijie Chen, Chang-Shou Lin and Yifan Yang. SIGMA 18 (2022), 013, 50 pages

In this paper, we study third-order modular ordinary differential equations (MODE for short) of the following form ′′′ + ₂()′ + ₃() = 0, ∈ ℍ = { ∈ ℂ | Im > 0}, where ₂() and ₃() − 1/2′₂() are meromorphic modular forms on SL(2, ℤ) of weight 4 and 6, respectively. We show that any quasimodular for...