Metrics with positive constant curvature and modular differential equations

Jia-Wei Guo, Chang-Shou Lin, Yifan Yang

In this paper, we consider the problem when a differential equation y"(z)=Q(z)y(z) is Fuchsian on H* and apparent on H, where Q(z) is a meromorphic modular form of weight 4 on SL(2…