Complex Pisot numbers in algebraic number fields

Abstract

Let P(K) be the set of Pisot numbers generating a real algebraic number field K over the field of rationals Q. Then, a result of Meyer implies that P(K) is relatively dense in the interval [1,∞) and a theorem of Pisot gives that P(K) contains units, whenever K≠Q. In the present note, we prove analogous results for the set of complex Pisot numbers generating a non-real number field K′ over Q when K′ is neither a quadratic field nor a CM-field.