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Mathematics of Computation

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Arithmetic $(1;e)$-curves and Belyĭ maps

Author: Jeroen Sijsling
Journal: Math. Comp. 81 (2012), 1823-1855
MSC (2010): Primary 14H57; Secondary 14G35, 14Q05, 34B30
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 $(1;e)$ 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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Additional Information

Jeroen Sijsling
Affiliation: Mathematisch Instituut Universiteit Utrecht, Postbus 80010, 3508TA Utrecht, The Netherlands
Address at time of publication: IRMAR–Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cédex, France
MR Author ID: 974789
ORCID: 0000-0002-0632-9910

Received by editor(s): October 13, 2010
Received by editor(s) in revised form: March 24, 2011
Published electronically: January 23, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.