On the Łojasiewicz numbers, II

Abstract

For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent L 0 ( f ) defined to be the smallest θ > 0 such that | grad f ( z ) | ⩾ c | z | θ near 0 ∈ C 2 for some c > 0 . The numbers L 0 ( f ) are rational. In this Note we discuss the interplay between arithmetical properties of the rationals L 0 ( f ) and topological properties of plane curve singularities f = 0 . To cite this article: E. García Barroso et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).