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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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


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
  • Email:
  • Received by editor(s): October 13, 2010
  • Received by editor(s) in revised form: March 24, 2011
  • Published electronically: January 23, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 1823-1855
  • MSC (2010): Primary 14H57; Secondary 14G35, 14Q05, 34B30
  • DOI:
  • MathSciNet review: 2904604