Article contents
ON THE MODULARITY OF SOLUTIONS TO CERTAIN DIFFERENTIAL EQUATIONS OF HYPERGEOMETRIC TYPE
Published online by Cambridge University Press: 15 September 2021
Abstract
We answer some questions in a paper by Kaneko and Koike [‘On modular forms arising from a differential equation of hypergeometric type’, Ramanujan J. 7(1–3) (2003), 145–164] about the modularity of the solutions of a certain differential equation. In particular, we provide a number-theoretic explanation of why the modularity of the solutions occurs in some cases and does not occur in others. This also proves their conjecture on the completeness of the list of modular solutions after adding some missing cases.
Keywords
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
References
- 1
- Cited by