Geodesic
Hermite–Padé approximants for meromorphic functions on a compact Riemann surface
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 4, pp. 671-706 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the limiting distribution of the zeros and the asymptotic behaviour of the Hermite–Padé polynomials of the first kind is considered for a system of germs $[1,f_{1,\infty},\dots,f_{m,\infty}]$ of meromorphic functions $f_j$, $j=1,\dots,m$, on an $(m+1)$-sheeted Riemann surface ${\mathfrak R}$. Nuttall's approach to the solution of this problem, based on a particular ‘Nuttall’ partition of ${\mathfrak R}$ into sheets, is further developed. Bibliography: 36 titles.
Keywords: distribution of zeros, convergence in capacity.
Mots-clés : rational approximants, Hermite–Padé polynomials 
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A. V. Komlov; R. V. Palvelev; S. P. Suetin; E. M. Chirka. Hermite–Padé approximants for meromorphic functions on a compact Riemann surface. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 72 (2017) no. 4, pp. 671-706. http://geodesic.mathdoc.fr/item/RM_2017_72_4_a2/

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