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Integral points on elliptic curves over number fields

Published online by Cambridge University Press:  01 July 1997

N. P. SMART  and
N. M. STEPHENS
N. P. SMART
Affiliation:
Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent CT2 7NF
N. M. STEPHENS
Affiliation:
Department of Mathematical and Computing Sciences, Goldsmiths College, University of London, New Cross, London SE14 6NW
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Abstract

In recent years there has been an interest in using elliptic logarithms to find integral points on elliptic curves defined over the rationals, see [23], [17], [6] and [12]. This has been partly due to work of David [5], who gave an explicit lower bound for linear forms in elliptic logarithms. Previously, integral points on elliptic curves had been found by Siegel's method; that is, a reduction to a set of Thue equations which could be solved, in principle, by the methods in [19]. For examples of this method see [3], [7], [16], [18], [21], [22] and [8]. Other techniques can be used to find all integral points in some special cases, see, for instance, [14].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 9 - 16
Copyright
Cambridge Philosophical Society 1997

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