On Modular Forms Arising from a Differential Equation of Hypergeometric Type
By Masanobu Kaneko, M. Koike. 2002
88 citations recorded by the source corpus.
Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a3545f951b313e91eae6b571430d11758045cb4a
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- 2-Dimensional vector-valued modular forms (2008, background): “We mention explicitly the paper of Kaneko and Koike [ 3 ], which has a more arithmetic focus than the present paper.”
- Hypergeometric series, modular linear differential equations and vector-valued modular forms (2015, methodology): “For each integer k, consider the following MLDE, which is studied in the papers [18], [19] and [46]:”
- Vertex operator algebras, Higgs branches, and modular differential equations (2017, methodology): “We note here that more beautiful expressions for the vacuum characters of these algebras have been presented in [17], using methods described in [96, 97].”