Explicit lower bounds for the height in Galois extensions of number fields

Abstract

Amoroso and Masser proved that for every real $\epsilon >0$, there exists a constant $c(\epsilon )>0$, such that for every algebraic number $\alpha$ with $\mathbb{Q}(\alpha )/\mathbb{Q}$ being a Galois extension, the height of $\alpha$ is either 0 or at least $c(\epsilon )[\mathbb{Q}(\alpha ):\mathbb{Q}{]}^{-\epsilon }$. In this article we establish an explicit version of this theorem.

Final version, to appear in the Journal de Théorie des Nombres de Bordeaux