Geodesic
The Gonchar--Chudnovskies conjecture and a functional analogue of the Thue--Siegel--Roth theorem
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 2, pp. 297-318

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This article examines the Gonchar–Chudnovskies conjecture about the limited size of blocks of diagonal Padé approximants of algebraic functions. The statement of this conjecture is a functional analogue of the famous Thue–Siegel–Roth theorem. For algebraic functions with branch points in general position, we will show the validity of this conjecture as a consequence of recent results on the uniform convergence of the continued fraction for an analytic function with branch points. We will also discuss related problems on estimating the number of “spurious” (“wandering”) poles for rational approximations (Stahl’s conjecture), and on the appearance and disappearance of defects (Froissart doublets). 
@article{MMO_2022_83_2_a4,
     author = {A. I. Aptekarev and M. Yattselev},
     title = {The {Gonchar--Chudnovskies} conjecture and a functional analogue of the {Thue--Siegel--Roth} theorem},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {297--318},
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     volume = {83},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2022_83_2_a4/}
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A. I. Aptekarev; M. Yattselev. The Gonchar--Chudnovskies conjecture and a functional analogue of the Thue--Siegel--Roth theorem. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 2, pp. 297-318. http://geodesic.mathdoc.fr/item/MMO_2022_83_2_a4/