On Singular Points of Meromorphic Functions Determined by Continued Fractions

Abstract

It is shown that Leighton’s conjecture about singular points of meromorphic functions represented by C-fractions K^∞_n=1(a_nz^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 K^∞_n=1(a_nA_n(z)/1), where A₁,A₂,... is a sequence of polynomials with limit distribution of zeros whose degrees tend to infinity.