On a New Approach to the Problem of Distribution of Zeros of Hermite—Padé Polynomials for a Nikishin System

Аннотация

A new approach to the problem of the zero distribution of type I Hermite—Padé polynomials for a pair of functions f₁, f₂ forming a Nikishin system is discussed. Unlike the traditional vector approach, we give an answer in terms of a scalar equilibrium problem with harmonic external field which is posed on a two-sheeted Riemann surface.