Geodesic
On a~new approach to the problem of distribution of zeros of Hermite--Pad\'e polynomials for a~Nikishin system
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 259-275

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A new approach to the problem of the zero distribution of type I Hermite–Padé polynomials for a pair of functions $f_1,f_2$ forming a Nikishin system is discussed. Unlike the traditional vector approach, we give an answer in terms of a scalar equilibrium problem with harmonic external field which is posed on a two-sheeted Riemann surface.
Keywords: Hermite–Padé polynomials, non-Hermitian orthogonal polynomials, distribution of zeros. 
@article{TM_2018_301_a18,
     author = {S. P. Suetin},
     title = {On a~new approach to the problem of distribution of zeros of {Hermite--Pad\'e} polynomials for {a~Nikishin} system},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {259--275},
     publisher = {mathdoc},
     volume = {301},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_301_a18/}
}
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S. P. Suetin. On a~new approach to the problem of distribution of zeros of Hermite--Pad\'e polynomials for a~Nikishin system. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 259-275. http://geodesic.mathdoc.fr/item/TM_2018_301_a18/