Approximation diophantienne dans les corps de series en plusieurs variables

Abstract

We give here a result of diophantine approximation between ${Ø}_N$, the ring of power series in several variables, and the completion of the valuation ring that dominates ${Ø}_N$ for the $\m$-adic topology. We deduce from this that the Artin function of a homogenous polynomial in two variables is bounded by an affine function, which can be interpreted in term of a Lojasiewicz inequality on the wedges space.

to appear in Annales de l'Institut Fourier, few changes following referee's comments