Mahler measure of a difference of two conjugates (Q2313197)

Let \(\alpha\) be an algebraic number of degree \(n\) over the rationals with conjugates \(\alpha_1, \dots, \alpha_n\). The ``house'' of \(\alpha\) is the maximal modulus of the conjugates of \(\alpha\). Suppose that \(\beta = \alpha_1 - \alpha_2\) and that \(\beta\) is of degree \(d = n(n-1)\). Let \(M(\beta)\) denote the Mahler measure of \(\beta\). The author shows that there is a constant \(c > 1\) which depends only on the house of \(\alpha\) such \(M(\beta) > c^d\).