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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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The maximal rank of elliptic Delsarte surfaces
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by Bas Heijne PDF
Math. Comp. 81 (2012), 1111-1130 Request permission

Abstract:

Shioda described a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over $k(t)$. In this article we find all elliptic curves over $k(t)$ for which his method is applicable. For these curves we also compute the maximal Mordell-Weil rank.
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Additional Information
  • Bas Heijne
  • Affiliation: The Johann Bernoulli Institute for Mathematics and Computer Science (JBI), University of Groningen, P. O. Box 407, 9700AK Groningen, the Netherlands
  • Email: b.l.heijne@rug.nl
  • Received by editor(s): July 9, 2010
  • Received by editor(s) in revised form: January 14, 2011
  • Published electronically: August 4, 2011
  • Additional Notes: The author would like to thank Jaap Top for several fruitful discussions
    This work was supported by a grant of the Netherlands Organization for Scientific Research (NWO)
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 1111-1130
  • MSC (2010): Primary 11G05, 14J27
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02529-9
  • MathSciNet review: 2869052