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
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
on transverse curves in
, 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
. We also give some explicit examples. This result generalises from rank 1 to rank
previous results of S. Checcoli, F. Veneziano and the author.
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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MDPI and ACS Style
Viada, E. Lattices and Rational Points. Mathematics 2017, 5, 36.
Viada E. Lattices and Rational Points. Mathematics. 2017; 5(3):36.
Viada, Evelina. 2017. "Lattices and Rational Points." Mathematics 5, no. 3: 36.
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