The Ramanujan Journal

, Volume 7, Issue 1, pp 145–164

On Modular Forms Arising from a Differential Equation of Hypergeometric Type

  • Masanobu Kaneko
  • Masao Koike

DOI: 10.1023/A:1026291027692

Cite this article as:
Kaneko, M. & Koike, M. The Ramanujan Journal (2003) 7: 145. doi:10.1023/A:1026291027692


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.

modular/quasimodular formshypergeometric differential equation

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Masanobu Kaneko
    • 1
  • Masao Koike
    • 2
  1. 1.Graduate School of MathematicsKyushu University 33FukuokaJapan
  2. 2.Graduate School of MathematicsKyushu University, RopponmatsuFukuokaJapan