6533b7d4fe1ef96bd12628d2

RESEARCH PRODUCT

Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra

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We give an upper estimate for the Łojasiewicz exponent $\ell(J,I)$ of an ideal $J\subseteq A(K^{n})$ with respect to another ideal I in the ring $A(K^{n})$ of germs analytic functions $f$ : $(K^{n},\mathrm{O})\rightarrow K$ , where $K=C$ or $R$ , using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent $\alpha_{0}(f)$ of a germ $f\in A(K^{n})$ that can be applied when $f$ is Newton degenerate with respect to its Newton polyhedron.