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Mathematics 2017, 5(3), 36; doi:10.3390/math5030036

Lattices and Rational Points

Mathematisches Institut, Georg-August-Universität, Bunsenstraße 3–5, D-D-37073 Göttingen, Germany
Received: 12 June 2017 / Revised: 4 July 2017 / Accepted: 4 July 2017 / Published: 9 July 2017
(This article belongs to the Special Issue Geometry of Numbers)
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Abstract

In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex Multiplication (CM). We then apply our result to give a method for finding the rational points on such curves, when E has Q -rank N - 1 . We also give some explicit examples. This result generalises from rank 1 to rank N - 1 previous results of S. Checcoli, F. Veneziano and the author. View Full-Text
Keywords: heights; rational points; curves; elliptic curves heights; rational points; curves; elliptic curves
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Viada, E. Lattices and Rational Points. Mathematics 2017, 5, 36.

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