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

TL;DR

This paper extends equidistribution results to sequences of algebraic sets not necessarily Galois stable, providing a quantitative theorem based on Mignotte's method, broadening the scope of Bilu's classical results.

Contribution

It introduces a quantitative equidistribution theorem for non-Galois stable sets, expanding the applicability of equidistribution principles in number theory.

Findings

Proves a quantitative equidistribution theorem for non-Galois stable sets.

Utilizes Mignotte's method to achieve the result.

Broadens understanding of algebraic set distributions.

Abstract

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