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-Padé 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.

中文翻译：

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标量平衡问题和II型Hermite-Padé多项式的零点的极限分布

使用两层Riemann曲面上的标量平衡问题，我们证明了对于形成Nishixin系统的一对函数，II型Hermite-Padé多项式的零的极限分布的存在。我们讨论了这里获得的结果与H. Stahl（1988）的一些结果之间的关系，并提出了数值实验的结果。本文的结果和第二作者的早期论文中获得的结果都与H.Stahl的结果和数值实验的结果均相符。