On the Distribution of Zeros of Faber Polynomials

Abstract

We prove a local version of the potential theoretic interpretation of the Erdos-Turan result on the distribution of zeros of complex algebraic polynomials with a given uniform norm on a closed subdisk of the open unit disk. As a consequence, we derive the exact rate of convergence of the unit counting measure for zeros of Faber polynomials with respect to a Dini-smooth Jordan arc to the equilibrium measure of the arc.