## Journal of the Mathematical Society of Japan

### Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra

Carles BIVlÀ-AUSINA

#### Abstract

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.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 655-668.

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.jmsj/1191418995

Digital Object Identifier
doi:10.2969/jmsj/1191418995

Mathematical Reviews number (MathSciNet)
MR1978215

Zentralblatt MATH identifier
1040.32024

Subjects