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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The maximal rank of elliptic Delsarte surfaces


Author: Bas Heijne
Journal: Math. Comp. 81 (2012), 1111-1130
MSC (2010): Primary 11G05, 14J27
Published electronically: August 4, 2011
MathSciNet review: 2869052
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02529-9
PII: S 0025-5718(2011)02529-9
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)
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.