On Motivic Zeta Functions and Stringy E-function via Embedded $\mathbb{Q}$-Resolution

TL;DR

This paper derives formulas for motivic zeta functions and stringy E-functions using embedded $ ext{Q}$-resolution, providing explicit calculations for specific classes of singularities and polynomials.

Contribution

It introduces new formulas for motivic zeta functions and stringy E-functions via embedded $ ext{Q}$-resolution, extending previous methods to semi-quasihomogeneous and non-degenerate polynomials.

Findings

Formulas for motivic zeta functions of semi-quasihomogeneous singularities

Determination of poles of zeta functions in dimension two

Explicit calculation of stringy E-functions for specific polynomial classes

Abstract

We provide the formula of motivic zeta function for semi-quasihomogeneous singularities and in dimension two, we determine the poles of zeta functions. We also give another formula for stringy E-function using embedded $\mathbb{Q}$-resolution, and we utilize it to calculate the stringy E-function for semi-quasihomogeneous polynomials and non-degenerate polynomials.