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

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