Arithmetic (1;𝑒)-curves and Belyĭ maps

Sijsling, Jeroen

doi:10.1090/S0025-5718-2012-02560-9

Arithmetic $(1;e)$-curves and Belyĭ maps
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Math. Comp. 81 (2012), 1823-1855 Request permission

Abstract:

Using the theory of Belyĭ 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.

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