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Mathematics of Computation

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Period computations for covers of elliptic curves


Author: Simon Rubinstein-Salzedo
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
Published electronically: January 13, 2014
MathSciNet review: 3223341
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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

DOI: https://doi.org/10.1090/S0025-5718-2014-02797-X
Keywords: Number theory, algebraic geometry
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.