# The {\L}ojasiewicz exponent for weighted homogeneous polynomials of two real variables

## TL;DR

This paper determines the exact {a}ojasiewicz exponent for isolated weighted homogeneous polynomials in two real variables based on their weights, providing precise mathematical characterization.

## Contribution

It provides a formula for the {a}ojasiewicz exponent of weighted homogeneous polynomials in two real variables, linking it explicitly to the polynomial's weights.

## Key findings

- Exact {a}ojasiewicz exponent values derived for the class of polynomials.
- Explicit relationship established between weights and exponent.
- Enhances understanding of singularity behavior in real polynomial functions.

## Abstract

The purpose of this paper is to give the exact value of the {\L}ojasiewicz exponent for an isolated weighted homogeneous polynomials of two real variaibles in terms of its weights.