On the maximal conjugate of a totally real algebraic integer

Let α be an algebraic integer of degreed whosed conjugates are all real. We give a lower bound for the absolute value of conjugates of α in terms ofd and of the number of conjugates outside the interval −2; 2]. Combining this with a lower bound for Mahler's measure of a polynomial, we obtain a lower bound for the maximal conjugate of a totally real algebraic integer. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 1, pp. 18–25, January–March, 1997.