The Weil height in terms of an auxiliary polynomial

Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $α$ under certain assumptions on $α$. 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.

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