On Modular Forms Arising from a Differential Equation of Hypergeometric Type
Graduate School of MathematicsKyushu University 33
Graduate School of MathematicsKyushu University, Ropponmatsu
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.