On modular solutions of certain modular differential equation and supersingular polynomials
We extend the results of Kaneko–Zagier and Baba–Granath on relations of supersingular polynomials and solutions of certain second-order modular differential equations.
KeywordsModular form Supersingular polynomials Hypergeometric series
Mathematics Subject Classification11F11 11F25
The author would like to thank Professor Masanobu Kaneko for helpful advice. He also thanks the anonymous referee for valuable suggestions.
- 1.Kaneko, M., Zagier, D.: Supersingular j-invariants, hypergeometric series, and Atkin’s orthogonal polynomials. In: Computational Perspectives on Number Theory (Chicago, IL, 1995). AMS/IP Stud. Adv. Math., 7, pp. 97–126. American Mathematical Society, Providence, RI (1998)Google Scholar