Geodesic
Singular points of meromorphic functions defined by their expansion
Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1405-1416

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Leighton's well-known conjecture about singular points of a meromorphic function defined by its expansion in a general $C$-fraction is discussed. A theorem proved in the paper yields, in particular, this conjecture for an arbitrary non-decreasing sequence of exponents $\alpha_k\to\infty$. Bibliography: 7 titles. 
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     author = {A. A. Gonchar},
     title = {Singular points of meromorphic functions defined by their expansion},
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     number = {10},
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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_10_a0/}
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A. A. Gonchar. Singular points of meromorphic functions defined by their expansion. Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1405-1416. http://geodesic.mathdoc.fr/item/SM_2006_197_10_a0/