Arithmetic (1;𝑒)-curves and Belyĭ maps

Sijsling, Jeroen

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

Arithmetic -curves and Belyĭ maps

Author: Jeroen Sijsling
Journal: Math. Comp. 81 (2012), 1823-1855
MSC (2010): Primary 14H57; Secondary 14G35, 14Q05, 34B30
DOI: https://doi.org/10.1090/S0025-5718-2012-02560-9
Published electronically: January 23, 2012
MathSciNet review: 2904604
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Abstract: Using the theory of Belyĭ maps, we calculate the algebraic curves associated to the Fuchsian groups of signature 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 -groups that are arithmetic.

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