Bornes effectives des fonctions d'approximation des solutions formelles d'\'equations binomiales

Abstract

The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the Weierstrass Preparation Theorem, we apply this effective result to binomial equations. We prove that the Artin function of a system of binomial equations is bounded by a doubly exponential function in general and that it is bounded by an affine function if the order of the approximated solutions is bounded.