Accessory Parameters for Four-Punctured Spheres
Number Theory
2022-03-29 v3 Classical Analysis and ODEs
Complex Variables
Abstract
We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This gives an effective method to compute the uniformizing differential equation. As an application, we compute numerically and study the local expansion of the real-analytic function associating to a four-punctured sphere the value of its uniformizing parameter, and make some observations on its coefficients.
Cite
@article{arxiv.2004.02971,
title = {Accessory Parameters for Four-Punctured Spheres},
author = {Gabriele Bogo},
journal= {arXiv preprint arXiv:2004.02971},
year = {2022}
}