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arXiv · 2004.02971

Accessory Parameters for Four-Punctured Spheres

Gabriele Bogo
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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.

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Gabriele Bogo. 2020-04-06. Accessory Parameters for Four-Punctured Spheres. https://doi.org/10.3842/sigma.2022.024

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