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Mathematical Notes

, Volume 103, Issue 3–4, pp 527–536 | Cite as

On Singular Points of Meromorphic Functions Determined by Continued Fractions

  • V. I. Buslaev
Article
  • 16 Downloads

Abstract

It is shown that Leighton’s conjecture about singular points of meromorphic functions represented by C-fractions Kn=1(a n z αn /1) with exponents α1, α2,... tending to infinity, which was proved by Gonchar for a nondecreasing sequence of exponents, holds also for meromorphic functions represented by continued fractions Kn=1(a n A n (z)/1), where A1,A2,... is a sequence of polynomials with limit distribution of zeros whose degrees tend to infinity.

Keywords

continued fraction Hankel determinant transfinite diameter meromorphic continuation 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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