On computing Belyi maps.(English)Zbl 1364.11127

Numéro consacré au trimestre “Méthodes arithmétiques et applications”, automne 2013. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2014, 1, 73-131 (2014).
Summary: We survey methods to compute three-point branched covers of the projective line, also known as Belyi maps. These methods include a direct approach, involving the solution of a system of polynomial equations, as well as complex analytic methods, modular forms methods, and $$p$$-adic methods. Along the way, we pose several questions and provide numerous examples.
For the entire collection see [Zbl 1301.11002].

MSC:

 11G32 Arithmetic aspects of dessins d’enfants, Belyĭ theory 11Y40 Algebraic number theory computations 14H57 Dessins d’enfants theory
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