Geodesic
On Singular points of Meromorphic Functions Determined by Continued Fractions
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 490-502

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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.
Keywords: continued fraction, Hankel determinant, transfinite diameter, meromorphic continuation. 
@article{MZM_2018_103_4_a1,
     author = {V. I. Buslaev},
     title = {On {Singular} points of {Meromorphic} {Functions} {Determined} by {Continued} {Fractions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {490--502},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a1/}
}
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V. I. Buslaev. On Singular points of Meromorphic Functions Determined by Continued Fractions. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 490-502. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a1/