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Quantitative Siegel's theorem for Galois coverings

Published online by Cambridge University Press:  04 December 2007

YURI F. BILU
YURI F. BILU
Affiliation:
Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-53225 Bonn, Germany
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Abstract

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It is known that Siegel's theorem on integral points is effective for Galois coverings of the projective line. In this paper we obtain a quantitative version of this result, giving an explicit upper bound for the heights of S-integral K-rational points in terms of the number field K, the set of places S and the defining equation of the curve. Our main tools are Baker's theory of linear forms in logarithms and the quantitative Eisenstein theorem due to Schmidt, Dwork and van der Poorten.

Keywords

Integral pointsSiegel's theoremBaker's methodramified coveringsEisenstein
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 2 , April 1997 , pp. 125 - 158
Copyright
© 1997 Kluwer Academic Publishers