The set of limit points for the conjugates of Pisot numbers

Based on the work of Boyd, we find all polynomials A with integer coefficients and such that [Formula: see text] and [Formula: see text] if [Formula: see text]. Combining this fact with Amara’s results, we prove that there are only finitely many Pisot numbers [Formula: see text], with one of the Galois conjugates of [Formula: see text] lying in the disc [Formula: see text]. The truth of this sheds some new light on a recent conjecture of Hare and Sidorov.