Lojasiewicz exponents, the integral closure of ideals and Newton polyhedra

摘要

We give an upper estimate for the Lojasiewicz exponent l(J, I) of an ideal J is contained in A(K~n) with respect to another ideal I in the ring A(K~n) of germs analytic functions f : (K~n, 0) → K, where K = C or R, using Newton polyhedrons. In particular, we give a method to estimate the Lojasiewicz exponent α_0(f) of a germ f ∈ A(K~n) that can be applied when f is Newton degenerate with respect to its Newton polyhedron.