On Modular Forms Arising from a Differential Equation of Hypergeometric Type |
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| Authors: | Kaneko Masanobu Koike Masao |
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| Institution: | (1) Graduate School of Mathematics, Kyushu University 33, Fukuoka, 812-8581, Japan;(2) Graduate School of Mathematics, Kyushu University, Ropponmatsu, Fukuoka, 810-8560, Japan |
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| Abstract: | 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. |
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| Keywords: | modular/quasimodular forms hypergeometric differential equation |
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