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
DOI:
https://doi.org/10.1090/S0025-5718-2012-02560-9
Published electronically:
January 23, 2012
MathSciNet review:
2904604
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Email:
sijsling@gmail.com
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.
