The Igusa local zeta function of certain Thom-Sebastiani type functions

TL;DR

This paper derives an explicit formula for the Igusa local zeta function associated with Thom-Sebastiani type sums of Newton non-critical polynomials, utilizing their Newton polyhedra for data description.

Contribution

It provides a novel explicit formula for Igusa local zeta functions of specific Thom-Sebastiani type functions based on Newton polyhedra.

Findings

Explicit formula for Igusa local zeta functions derived

Utilizes Newton polyhedra for data description

Applicable to Thom-Sebastiani type sums of polynomials

Abstract

In this paper, we give an explicit formula of the Igusa local zeta function of a Thom-Sebastiani type sum of two separated-variable Newton non-critical polynomials. Data for the description are available on their Newton polyhedra.