On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Masanobu Kaneko, Masao Koike

Research output: Contribution to journalArticle

31 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 1 2003

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Modular Forms
Fourier coefficients
Half-plane
Second order differential equation
Positivity
Differential equation
Invariant

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

On Modular Forms Arising from a Differential Equation of Hypergeometric Type. / Kaneko, Masanobu; Koike, Masao.

In: Ramanujan Journal, Vol. 7, No. 1-3, 01.03.2003, p. 145-164.

Research output: Contribution to journalArticle

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