On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Masanobu Kaneko, Masao Koike

Research output: Contribution to journalArticlepeer-review

38 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 languageEnglish
Pages (from-to)145-164
Number of pages20
JournalRamanujan Journal
Volume7
Issue number1-3
DOIs
Publication statusPublished - Mar 2003

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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