Abstract: We discuss Kronecker's theorem characterizing algebraic integers contained in the closed unit disk together with all conjugates, and related conjectures of Lehmer and of Schinzel-Zassenhaus. While the former conjecture remains open, the latter one was recently proved by Vesselin Dimitrov. We shall sketch his proof, and give a generalization that leads to a proof of some conjectures by David Boyd in the case of algebraic integers with conjugates symmetric in the unit circle.
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