Lattices and Rational Points

Evelina Viada
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Evelina Viada: Mathematisches Institut, Georg-August-Universität, Bunsenstraße 3–5, D-D-37073 Göttingen, Germany

Mathematics, 2017, vol. 5, issue 3, 1-16

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.

Keywords: heights; rational points; curves; elliptic curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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