Motivic invariant of real polynomial functions and Newton polyhedron

TL;DR

This paper introduces a method to compute real motivic zeta functions for polynomial functions using Newton polyhedra, revealing that weights are invariants under blow-Nash transformations for certain weighted homogeneous polynomials.

Contribution

It presents a novel approach to calculating real motivic zeta functions via Newton polyhedra and establishes weights as blow-Nash invariants for specific polynomial classes.

Findings

Computed real motivic zeta functions using Newton polyhedron techniques.

Proved weights are blow-Nash invariants for convenient weighted homogeneous polynomials in three variables.

Established invariance properties for polynomial weights under blow-Nash transformations.

Abstract

We propose a computation of real motivic zeta functions for real polynomial functions, using Newton polyhedron. As a consequence we show that the weights are blow-Nash invariants of convenient weighted homogeneous polynomials in three variables.