Equidistribution for sets which are not necessarily Galois stable: On a theorem of Mignotte

An important result of Bilu deals with the equidistribution of the Galois orbits of a sequence $({\alpha }_n{)}_n$ in ${\bar{\mathbb{Q}}}^{\ast }$. Here, we prove a quantitative equidistribution theorem for a sequence of finite subsets in ${\bar{\mathbb{Q}}}^{\ast }$ which are not necessarily stable by Galois action. We follow a method of Mignotte.