Bernstein polynomial and value set of differentials for plane branches

In this work, we study the relation between the roots of the Bernstein polynomial $\tilde{b}$ and the value set of differentials $\mathrm{\Lambda }$ for plane branches. For plane branches defined by semiquasihomogeneous polynomial we describe the set of common roots of $\tilde{b}$ sharing by every branch with a fixed $\mathrm{\Lambda }$ set.