Geodesic
Scalar approaches to the limit distribution of the zeros of~Hermite--Pad\'e polynomials for a~Nikishin system
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 80 (2025) no. 1, pp. 75-136

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The problem of the existence of a limit distribution of the zeros of Hermite–Padé polynomials for a pair of functions forming a Nikishin system is discussed. Two new scalar methods are proposed for the investigation of this problem. The first is based on a potential-theoretic equilibrium problem stated on a two-sheeted Riemann surface and on the use of the Gonchar–Rakhmanov–Stahl ($\operatorname{GRS}$-)method in treating this problem. The second method is based on the existence of a three-sheeted Riemann surface with Nuttall partition into sheets which is associated with a given pair of functions $f$, $f^2$, and it uses only the maximum principle for subharmonic functions. The connection of these methods and the results obtained with Stahl's methods and results of 1987–88 is discussed. Results of numerical experiments are presented. Bibliography: 109 titles.
Keywords: Hermite–Padé polynomials, Nikishin system, potential theory, equilibrium problem, Riemann surfaces. 
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S. P. Suetin. Scalar approaches to the limit distribution of the zeros of~Hermite--Pad\'e polynomials for a~Nikishin system. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 80 (2025) no. 1, pp. 75-136. http://geodesic.mathdoc.fr/item/RM_2025_80_1_a2/