Dessins on Modular Curves
Abstract
Given a finite index subgroup of PSL2(Z), we investigate Belyi functions on the corresponding modular curve X() by introducing two methods for constructing such functions. Numerous examples have been worked out completely and as an application, we have derived modular equations for 0(2),0(3) and several special values of the j-function by a new method based on the theory of Belyi functions and dessin d'enfants.
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