Zeros of the derivatives of Faber polynomials associated with a universal covering map

For a compact set E⊂C with connected complement, we study asymptotic behavior of normalized zero counting measures {μk} of the derivatives of Faber polynomials associated with E. For example if E has empty interior, we prove that {μk} converges in the weak-star topology to a probability measure whose support is the boundary of g(D), where is a universal covering map such that g(∞)=∞ and D is the Dirichlet domain associated with g and centered at ∞.Our results are counterparts of those of Kuijlaars and Saff [Asymptotic distribution of the zeros of Faber polynomials, Math. Proc. Cambridge Philos. Soc. 118 (1995) 437–447] on zeros of Faber polynomials.