Computing motivic zeta functions on log smooth models

TL;DR

This paper presents an explicit formula for motivic zeta functions using log smooth models, generalizing classical formulas and reducing candidate poles, with applications to Newton non-degenerate polynomials.

Contribution

It introduces a new explicit formula for motivic zeta functions based on log smooth models, extending previous results for snc-models.

Findings

The formula reduces the number of candidate poles compared to classical methods.

It encompasses the case of Newton non-degenerate polynomials as a special case.

Provides a more general framework for computing motivic zeta functions.

Abstract

We give an explicit formula for the motivic zeta function in terms of a log smooth model. It generalizes the classical formulas for snc-models, but it gives rise to much fewer candidate poles, in general. As an illustration, we explain how the formula for Newton non-degenerate polynomials can be viewed as a special case of our results.