A propos de la fonction de Artin en dimension N⩾2

In this Note we give a counter-example to a generalization in dimension N⩾2 of a result of Hickel in dimension 1 [Am. J. Math. 115 (1993) 1299-1334] which relates the Artin function of a germ of holomorphic function to the Artin function of its Jacobian ideal. Such links are important in order to prove the linear Artin approximation theorem that has been conjectured fifteen years ago [Spivakovsky, Proceedings of the II SBWAG, Santiago de Compostela 54 (1990) 237-254]. To cite this article: G. Rond, C. R. Acad. Sci. Paris, Ser. I 340 (2005).