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 $\mathscr K _{n=1}^\infty(a_nz^{\alpha_n}/1)$ with exponents $\alpha_1,\alpha_2,\dots$ tending to infinity, which was proved by Gonchar for a nondecreasing sequence of exponents, holds also for meromorphic functions represented by continued fractions $\mathscr K _{n=1}^\infty(a_nA_n(z)/1)$, where $A_1,A_2,\dots$ is a sequence of polynomials with limit distribution of zeros whose degrees tend to infinity.