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ON THE MODULARITY OF SOLUTIONS TO CERTAIN DIFFERENTIAL EQUATIONS OF HYPERGEOMETRIC TYPE.
- Source :
-
Bulletin of the Australian Mathematical Society . Jun2022, Vol. 105 Issue 3, p385-391. 7p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 105
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 156803898
- Full Text :
- https://doi.org/10.1017/S0004972721000721