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Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite–Padé Polynomials of Type II N. R. Ikonomova, S. P. Suetinb a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev str., Sofia, 1113, Bulgaria b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia 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–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.
DOI: https://doi.org/10.4213/tm4080   Full text:
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English version: Proceedings of the Steklov Institute of Mathematics, 2020, 309, Bibliographic databases:   
UDC: 517.53 Received: Revised: Accepted: Citation: N. R. Ikonomov, S. P. Suetin, “Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite–Padé Polynomials of Type II”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Tr. Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 
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