Approximations diophantiennes dans un corps local
Ce travail est essentiellement consacré à la construction d’exemples effectifs de couples de nombres réels à constantes de Markov finies, tels que et soient -linéairement indépendants, et satisfaisant à la conjecture de Littlewood.
In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type , where q is a power of p.
We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in -adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.
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