Quelques résultats sur les approximations diophantiennes
Quelques résultats sur les approximations diophantiennes
Rational approximations to algebraic Laurent series with coefficients in a finite field
We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series for which...
Séries d'Eisenstein et transcendance
Simultane diophantische Approximationen abhängiger Größen in mehreren Metriken
Simultaneous approximation of zero by values of integral polynomials with respect to different valuations
Simultaneous Diophantine Approximation for Algebraic Functions in Positive Characteristic.
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations
We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve with respect to the different valuations. It is an extension of the author’s earlier results.
Some applications of a non-Archimedean analogue of Descartes' rule of signs
Sous-groupes à plusieurs paramètres -adiques de variétés abéliennes
Sous-groupes analytiques de variétés de groupe et théorème de Brumer
Sur le developpement de ... en fraction continue p-adique.
Sur un théorème de M. Mahler
The Approximation of Solutions to Linear Homogeneous Differential Equations by Rational Functions.
The Farey Series of polynomials over a finite field.
The metric simultaneous diophantine approximations over formal power series
We discuss the metric theory of simultaneous diophantine approximations in the non-archimedean case. First, we show a Gallagher type 0-1 law. Then by using this theorem, we prove a Duffin-Schaeffer type theorem.
The number of subspaces occurring in the p-adic subspace theorem in diophantine approximation.
The quantitative subspace theorem for number fields
Théorème de Koksma en -adique
Transcendance dans le domaine -adique