Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite-Padé Polynomials of Type II

Abstract

Using the scalar equilibrium problem posed on the two-sheeted Riemann surface, we prove the existence of a limit distribution of the zeros of Hermite-Pade polynomials of type II for a pair of functions forming a Nikishin system. We discuss the relation of the results obtained here to some results of H. Stahl (1988) and present results of numerical experiments. The results of the present paper and those obtained in earlier papers of the second author are shown to be in good accordance with both H. Stahl’s results and results of numerical experiments.