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

Abstract

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