Abstract
1. Introduction. A well-known theorem of Siegel(5) states that there exist only a finite number of integer points on any curve of genus ≥ 1. Siegel's proof, published in 1929, depended, inter alia, on his earlier work concerning rational approximations to algebraic numbers and on Weil's recently established generalization of Mordell's finite basis theorem. Both of these possess a certain non-effective character and thus it is clear that Siegel's argument cannot provide an algorithm for determining all the integer points on the curve. The purpose of the present paper is to establish such an algorithm in the case of curves of genus 1.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
1. Bounds for the solutions of the hyperelliptic equation
2. (5) Siegel C. L. Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. 1929, No. 1.
3. Introduction to the Theory of Algebraic Functions of One Variable
4. Construction of rational functions on curves.;Coates;Proc. Cambridge Philos. Soc.
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