Geodesic
Distribution of the zeros of Pad\'e polynomials and analytic continuation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 5, pp. 901-951

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The problem of analytic continuation of a multivalued analytic function with finitely many branch points on the Riemann sphere is discussed. The focus is on Padé approximants: classical (one-point) Padé approximants, multipoint Padé approximants, and Hermite–Padé approximants. The main result is a theorem on the distribution of zeros and the convergence of the Hermite–Padé approximants for a system $[1,f,f^2]$, where $f$ is a multivalued function in the so-called Laguerre class $\mathscr{L}$. Bibliography: 128 titles.
Keywords: analytic continuation, continued fractions, Padé polynomials, Hermite–Padé polynomials, distribution of zeros, GRS-method, convergence in capacity.
Mots-clés : orthogonal polynomials, rational approximants 
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     author = {S. P. Suetin},
     title = {Distribution of the zeros of {Pad\'e} polynomials and analytic continuation},
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S. P. Suetin. Distribution of the zeros of Pad\'e polynomials and analytic continuation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 5, pp. 901-951. http://geodesic.mathdoc.fr/item/RM_2015_70_5_a2/