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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computation of highly ramified coverings
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by Raimundas Vidūnas and Alexander V. Kitaev PDF
Math. Comp. 78 (2009), 2371-2395 Request permission

Abstract:

An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degrees 11, 12, and 20 are explicitly constructed. We demonstrate how these coverings can be used for computation of several algebraic solutions of the sixth Painlevé equation.
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Additional Information
  • Raimundas Vidūnas
  • Affiliation: Department of Mathematics, Kyushu University, Fukuoka 812-8581, Japan
  • Address at time of publication: Department of Mathematics, Kobe University, Rokko-dai 1-1, Nada-ku, Kobe 657-8501, Japan
  • Email: rvidunas@gmail.com
  • Alexander V. Kitaev
  • Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
  • Address at time of publication: Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
  • Email: kitaev@pdmi.ras.ru
  • Received by editor(s): June 21, 2007
  • Received by editor(s) in revised form: October 16, 2008
  • Published electronically: February 11, 2009
  • Additional Notes: The first author was supported by the 21st Century COE Programme “Development of Dynamic Mathematics with High Functionality” of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
    The second author was supported by JSPS grant-in-aide No. $14204012$.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 2371-2395
  • MSC (2000): Primary 57M12, 34M55; Secondary 33E17
  • DOI: https://doi.org/10.1090/S0025-5718-09-02233-9
  • MathSciNet review: 2521293