2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94861We 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 commentsAlgebraic GeometryComplex Variables14B05, 32S99, 11J25text