On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system

A new approach to the problem of the zero distribution of type I Hermite–Padé polynomials for a pair of functions $f_1,f_2$ 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.