We give an upper estimate for the Łojasiewicz exponent of an ideal with respect to another ideal I in the ring of germs analytic functions : , where or , using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent of a germ that can be applied when is Newton degenerate with respect to its Newton polyhedron.
Carles BIVlÀ-AUSINA. "Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra." J. Math. Soc. Japan 55 (3) 655 - 668, July, 2003. https://doi.org/10.2969/jmsj/1191418995