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Israel Journal of Mathematics

, Volume 90, Issue 1–3, pp 235–252 | Cite as

Effective analysis of integral points on algebraic curves

  • Yuri Bilu
Article

Abstract

LetK be an algebraic number field,SS \t8 a finite set of valuations andC a non-singular algebraic curve overK. LetxK(C) be non-constant. A pointPC(K) isS-integral if it is not a pole ofx and |x(P)| v >1 impliesvS. It is proved that allS-integral points can be effectively determined if the pair (C, x) satisfies certain conditions. In particular, this is the case if
  1. (i)

    x:CP1 is a Galois covering andg(C)≥1;

     
  2. (ii)

    the integral closure of\(\bar Q\)[x] in\(\bar Q\)(C) has at least two units multiplicatively independent mod\(\bar Q\)*.

     

This generalizes famous results of A. Baker and other authors on the effective solution of Diophantine equations.

Keywords

Integral Point Algebraic Curf Diophantine Equation Galois Covering Algebraic Number Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1995

Authors and Affiliations

  • Yuri Bilu
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceBen-Gurion UniversityBeer ShevaIsrael
  2. 2.Mathématiques StochastiquesUniversité Bordeaux 2Bordeaux CedexFrance

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