Geodesic
Chebyshev representation for rational functions
Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1579-1598

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An effective representation is obtained for rational functions all of whose critical points, apart from $g-1$, are simple and their corresponding critical values lie in a four-element set. Such functions are described using hyperelliptic curves of genus $g\geqslant1$. The classical Zolotarëv fraction arises in this framework for $g=1$. Bibliography: 8 titles.
Keywords: rational approximation, Riemann surfaces, Abelian integrals.
Mots-clés : Zolotarëv fraction 
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     author = {A. B. Bogatyrev},
     title = {Chebyshev representation for rational functions},
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A. B. Bogatyrev. Chebyshev representation for rational functions. Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1579-1598. http://geodesic.mathdoc.fr/item/SM_2010_201_11_a1/