Mathematical Research Letters

Volume 20 (2013)

Number 2

Łojasiewicz inequality over the ring of power series in two variables

Pages: 325 – 337



Guillaume Rond (Institut de Mathématiques de Luminy, Faculté des Sciences de Luminy, Marseille, France)


We prove a Łojasiewicz type inequality for a system of polynomial equations with coefficients in the ring of formal power series in two variables. This result is an effective version of the Strong Artin Approximation Theorem. From this result, we deduce a bound of Artin functions of isolated singularities.

Published 3 December 2013