On modular forms arising from a differential equation of hypergeometric type

被引：55

作者：

Kaneko, M ^{[1
]}

Koike, M

机构：

[1] Kyushu Univ 33, Grad Sch Math, Fukuoka 8128581, Japan

[2] Kyushu Univ, Grad Sch Math, Fukuoka 8108560, Japan

来源：

RAMANUJAN JOURNAL | 2003年 / 7卷 / 1-3期

关键词：

modular/quasimodular forms; hypergeometric differential equation;

D O I：

10.1023/A:1026291027692

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：145 / 164

页数：20