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Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations
Author(s):
L.
Hajdu;
T.
Kovács.
Journal:
Math. Comp.
78
(2009),
1201-1210.
MSC (2000):
Primary 11G05;
Secondary 11Y50
Posted:
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  method a certain parameter  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  . 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:
10.1090/S0025-5718-08-02160-1
PII:
S 0025-5718(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
Posted:
July 1, 2008
Additional Notes:
Research supported in part by the Hungarian Academy of Sciences and by the OTKA grants T48791 and K67580.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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