On a conjecture of Schinzel and Zassenhaus

Abstract

A. Schinzel and H. Zassenhaus had the following conjecture regarding algebraic inte- gers: If α � 0 is an algebraic integer of degree n which is not a root of unity, then there exists a constant c > 0 such that |α | 1+ c , where |α | = max1in |αi|, α1 = α and α2,···,αn are the conjugates of α . We give some partial solutions to this conjecture in this paper via spectral properties.