Aspects effectifs d'analyse diophantienne

ABOUZAID, Mourad

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ABOUZAID, Mourad

Thèses de doctorat

Fecha de defensa

2006-07-03

Resumen en inglés

The first chapter of this thesis is about Lucas' and Lehmer's sequences. It is known that from rank 30 every Lucas' number (resp. Lehmer?s number) has a 'new' prime divisor. In this first chapter, we complete the list of pathological cases, began by P.M. VOUTIER, Yu. BILU and G. HANROT. In the second chapter we recall some definitions and proprietes of Weil's logarithmic heights and Puiseux' series. We use these in the two last chapter, in which we give explicite bound for the Weil?s height of algebraic solutions for some groups of diophantine equations. The third chapter is about a generalization and an improvement of Walsh' results on Skolem?s diophantine problem. In the last chapter, we give explicite bounds for the Weil's height of S-integral solutions of some generalization of Thue's famous equations.< Leer menos

Palabras clave

Mathématiques Pures

Lucas' numbers,

Lehmer's number

Weil height

Puiseux' series,

diophantine equations,

Skolem's problem

Thue's equations

URI

https://oskar-bordeaux.fr/handle/20.500.12278/25212

Centros de investigación

Thèses de l'Université de Bordeaux avant 2014

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