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Bornes effectives des fonctions d'approximation des solutions formelles d'équations binomiales
Guillaume Rond
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 Approxim…
Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin
Guillaume Rond
We interpret the Artin-Rees lemma and the Izumi theorem in term of Artin function and we obtain a stable version of the Artin-Rees lemma. We present different applications of these…
Sur la linearite de la fonction de Artin
Guillaume Rond
We give here a counter-example to a conjecture of Spivakovsky. M. Spivakovsky conjectured that the function that appears in the strong Artin approximation theorem is bounded by a l…
Theoreme d'approximation cylindrique dans le cas des anneaux analytiques
Guillaume Rond
This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.