Approximations of algebraic functions by rational ones – functional analogues of diophantine approximants
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 ε = 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
Publication language:russian, pages:24
Research direction:
Mathematical problems and theory of numerical methods
