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

Abstract

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

Here is the second version of the preprint "Bilu's equidistribution theorem over algebraic fields of infinite degree". The organization of this version is totally different because the main result of the first one partially follows from a recent preprint due to Doyle, Fili and Tobin, of which we were unaware