The Weil height in terms of an auxiliary polynomial

Abstract

Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $\alpha$ under certain assumptions on $\alpha$. We prove a theorem which introduces an auxiliary polynomial for giving lower bounds on the height of any algebraic number. Our theorem contains, as corollaries, a slight generalization of the above results as well as some new lower bounds in other special cases.