Hyperbolic uniformization of Fermat curves (Q861561)

Apart a reference and a word, I cite directly the authors' abstract : The ground-breaking research on the uniformization of curves was conducted at the beginning of the last century. Nevertheless, there are few examples in the literature of algebraic curves for which an explicit uniformization is known. In this article the authors obtain an explicit uniformization of the Fermat curves \(F_N\), for each \(N\geq 4\). The results presented here are based in part on an earlier study of the second author in which each Riemann surface \(F_N(\mathbb C)\) was described as a quotient of the complex disk by a Fuschian group \(\Gamma\).