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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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Period computations for covers of elliptic curves
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by Simon Rubinstein-Salzedo PDF
Math. Comp. 83 (2014), 2455-2470 Request permission

Abstract:

In this article, we construct algebraic equations for a curve $C$ and a map $f$ to an elliptic curve $E$, with pre-specified branching data. We do this by determining certain relations that the periods of $C$ and $E$ must satisfy and using these relations to approximate the coefficients to high precision. We then conjecture which algebraic numbers the coefficients are, and then we prove this conjecture to be correct.
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Additional Information
  • Simon Rubinstein-Salzedo
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
  • Email: simon.rubinstein-salzedo@dartmouth.edu
  • Received by editor(s): October 17, 2012
  • Received by editor(s) in revised form: January 17, 2013, and January 28, 2013
  • Published electronically: January 13, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2455-2470
  • MSC (2010): Primary 11G32, 11J70, 14H30, 14H52, 14Q05
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02797-X
  • MathSciNet review: 3223341