On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Masanobu Kaneko; Masao Koike

doi:10.1023/A:1026291027692

On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Masanobu Kaneko, Masao Koike

Research output: Contribution to journal › Article › peer-review

51 Citations (Scopus)

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.

Original language	English
Pages (from-to)	145-164
Number of pages	20
Journal	Ramanujan Journal
Volume	7
Issue number	1-3
DOIs	https://doi.org/10.1023/A:1026291027692
Publication status	Published - Mar 2003

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1023/A:1026291027692

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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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AB - 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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On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Abstract

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