Geodesic
Rational functions with two critical points of maximum multiplicity
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 6, pp. 185-208

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In this paper, we consider the functions on algebraic curves whose divisors have the form $nA-nC$. Combinatorial-topological and algebraic descriptions are introduced for exploring such functions. All Belyi functions with such divisor are described. The case of curves of genus 1 is considered in more detail. The number of Belyi functions with divisor $nA-nC$ is explicitly calculated. For general functions of this type on a curve of genus 1, we consider the space of the parameters and a method of its calculation that uses the Padé approximation. 
@article{FPM_2013_18_6_a11,
     author = {D. A. Oganesyan},
     title = {Rational functions with two critical points of maximum multiplicity},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {185--208},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_6_a11/}
}
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D. A. Oganesyan. Rational functions with two critical points of maximum multiplicity. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 6, pp. 185-208. http://geodesic.mathdoc.fr/item/FPM_2013_18_6_a11/