Zero distribution of incomplete Pade and Hermite-Pade approximations

We prove that a subsequence of the normalized zero counting measures of incomplete Pade approximants tend, as the degree of the numerators goes to infinity and that of the denominators remains bounded, to the uniform distribution on the largest circle centered at the origin inside of which the approximants converge in the sense of the Hausdorff content. As a consequence, a Jentzsch-Szego type theorem for row sequences of Hermite-Pade approximants is given. (C) 2015 Elsevier Inc. All rights reserved.