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.
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, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 174–197; Proc. Steklov Inst. Math., 309 (2020), 159–182
\Bibitem{IkoSue20}
\by N.~R.~Ikonomov, S.~P.~Suetin
\paper Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite--Pad\'e Polynomials of Type II
\inbook Modern problems of mathematical and theoretical physics
\bookinfo Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 309
\pages 174--197
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4080}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 309
\pages 159--182
\crossref{https://doi.org/10.1134/S0081543820030128}
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https://doi.org/10.4213/tm4080
https://www.mathnet.ru/eng/tm/v309/p174
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