Arithmetic (1; e)-curves and Belyi maps
Résumé
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.