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Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations


Authors: L. Hajdu and T. Kovács
Journal: Math. Comp. 78 (2009), 1201-1210
MSC (2000): Primary 11G05; Secondary 11Y50
DOI: https://doi.org/10.1090/S0025-5718-08-02160-1
Published electronically: July 1, 2008
MathSciNet review: 2476581
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Abstract: Stroeker and Tzanakis gave convincing numerical and heuristic evidence for the fact that in their $ \mathcal{E}llog$ method a certain parameter $ \lambda$ plays a decisive role in the size of the final bound for the integral points on elliptic curves. Furthermore, they provided an algorithm to determine the Mordell-Weil basis of the curve which corresponds to the optimal choice of $ \lambda$. In this paper we show that working with more Mordell-Weil bases simultaneously, the final bound for the integral points can be further decreased.


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Additional Information

L. Hajdu
Affiliation: University of Debrecen, Institute of Mathematics, and the Number Theory Research Group of the Hungarian Academy of Sciences, P.O. Box 12, H-4010 Debrecen, Hungary
Email: hajdul@math.klte.hu

T. Kovács
Affiliation: University of Debrecen, Institute of Mathematics, P.O. Box 12, H-4010 Debrecen, Hungary
Email: tundekov@gmail.com

DOI: https://doi.org/10.1090/S0025-5718-08-02160-1
Keywords: Elliptic curves, integral points, LLL-reduction
Received by editor(s): December 18, 2007
Received by editor(s) in revised form: March 12, 2008
Published electronically: July 1, 2008
Additional Notes: Research supported in part by the Hungarian Academy of Sciences and by the OTKA grants T48791 and K67580.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.