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.