Arithmetic (1; e)-curves and Belyi maps

Jeroen Sijsling (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Using the theory of Belyi maps, we calculate the algebraic curves associated to the Fuchsian groups of signature (1; e) that are commensurable with a triangle group, along with the Picard-Fuchs differential equations on these curves, which are related to pullbacks of hypergeometric differential equations. We focus particularly on the (1; e)-groups that are arithmetic.

Mots clés: Shimura curves; Fuschsian-groups; triangle groups; genus; subgroups; equations

Jeroen Sijsling. Arithmetic (1; e)-curves and Belyi maps. Mathematics of Computation, 2012, 81 (279), pp.1823-1855. ⟨hal-00716718⟩