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Keldysh Institute preprints, 2016, 084, 24 pages (Mi ipmp2158)  

Approximations of algebraic functions by rational ones — functional analogues of diophantine approximants

A. I. Aptekarev, M. L. Yattselev


Abstract: A goal of this note is to discuss applications of our result on asymptotics of the convergents of a continued fraction of an analytic function with branch points. We consider famous problems: on normality of the Pade approximants for algebraic functions (a functional analog of the Thue–Siegel–Roth theorem and $\varepsilon = 0$ Gonchar–Chudnovskies conjecture), on estimation of the number of spurious (wandering) poles of rational approximants for algebraic functions (Stahl conjecture), on appearance and disappearance of the Froissart doublets.

Keywords: rational approximants, algebraic functions, strong asymptotics, degree of the diophantine approximations.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025


DOI: https://doi.org/10.20948/prepr-2016-84

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Full text: http:/.../preprint.asp?id=2016-84&lg=r
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UDC: 517.53+517.9

Citation: A. I. Aptekarev, M. L. Yattselev, “Approximations of algebraic functions by rational ones — functional analogues of diophantine approximants”, Keldysh Institute preprints, 2016, 084, 24 pp.

Citation in format AMSBIB
\Bibitem{AptYat16}
\by A.~I.~Aptekarev, M.~L.~Yattselev
\paper Approximations of algebraic functions by rational ones~--- functional analogues of diophantine approximants
\jour Keldysh Institute preprints
\yr 2016
\papernumber 084
\totalpages 24
\mathnet{http://mi.mathnet.ru/ipmp2158}
\crossref{https://doi.org/10.20948/prepr-2016-84}


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