From Differential Values to Roots of the Bernstein-Sato Polynomial

Let $C$ be a cusp in $({\mathbb{C}}^2,\mathbf{0})$ with Puiseux pair $(n,m)$. This paper is devoted to show how the semimodule of differential values of $C$ determines a subset of the roots of the Bernstein-Sato polynomial of $C$. We add more precise results when the multiplicity of the cusp is $n\le 4$.