Newton weighted-Lê-Yomdin polynomials and $\mu$-Zariski pairs of surface singularities

We investigate surface singularities defined by weighted-Lê-Yomdin polynomials, with a particular focus on a specific subclass that we refer to as Newton weighted-Lê-Yomdin polynomials. In particular, using polynomials in this subclass, we develop a method to construct new $\mu$-Zariski pairs of surface singularities.