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

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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.

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Acknowledgments

The authors are grateful to the referee for a number of valuable comments that have improved the presentation of the results obtained in the paper.

Funding

The research of the second author was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00764.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev str., Sofia, 1113, Bulgaria

    N. R. Ikonomov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    S. P. Suetin

Authors
  1. N. R. Ikonomov
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  2. S. P. Suetin
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Corresponding authors

Correspondence to N. R. Ikonomov or S. P. Suetin.

Additional information

This article was submitted by the authors simultaneously in Russian and English

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 309, pp. 174–197.

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Ikonomov, N.R., Suetin, S.P. Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite-Padé Polynomials of Type II. Proc. Steklov Inst. Math. 309, 159–182 (2020). https://doi.org/10.1134/S0081543820030128

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  • DOI: https://doi.org/10.1134/S0081543820030128

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