Metrics with positive constant curvature and modular differential equations
Classical Analysis and ODEs
2021-11-01 v1 Number Theory
Abstract
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,Z) and H denotes the complex upper half-plane. Such a problem is closely related to the problem of the existence of a conformal metric with curvature 1/2 on H.
Keywords
Cite
@article{arxiv.2110.15580,
title = {Metrics with positive constant curvature and modular differential equations},
author = {Jia-Wei Guo and Chang-Shou Lin and Yifan Yang},
journal= {arXiv preprint arXiv:2110.15580},
year = {2021}
}
Comments
40 pages, accepted for publication on the Cambridge Journal of Mathematics