Geodesic
Convergence of Chebysh\"ev continued fractions for elliptic functions
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1807-1835

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Dumas's classical theorem on the behaviour of the Chebyshëv continued fraction corresponding to an elliptic function $f(z)=\sqrt{(z-e_1)\dotsb(z-e_4)}-z^2+z{(e_1+\dotsb+e_4)}/2$ holomorphic at $z=\infty$ is extended to a fairly general class of elliptic functions. The behaviour of the Chebyshëv continued fractions corresponding to functions in that class is characterized in terms relating to the mutual position of the branch points $e_1,\dots,e_4$. The proof is based on the investigation of the properties of the solution of a certain Riemann boundary-value problem on an elliptic Riemann surface. 
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     author = {S. P. Suetin},
     title = {Convergence of {Chebysh\"ev} continued fractions for elliptic functions},
     journal = {Sbornik. Mathematics},
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     number = {12},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_12_a2/}
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S. P. Suetin. Convergence of Chebysh\"ev continued fractions for elliptic functions. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1807-1835. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a2/