On Singular Points of Meromorphic Functions Determined by Continued Fractions

It is shown that Leighton’s conjecture about singular points of meromorphic functions represented by C-fractions K ∞ n =1 ( a n z αn /1) with exponents α 1 , α 2 ,... 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 n A n ( z )/1), where A 1 , A 2 ,... is a sequence of polynomials with limit distribution of zeros whose degrees tend to infinity.