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

International audience ; Amoroso and Masser proved that for every real ϵ > 0, there is 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 this article, we establish an explicit version of this theorem.