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arXiv · 1511.05346

How many Zolotarev fractions are there?

Andrei Bogatyrev
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Abstract

Known properties of Chebyshev polynomials are the following: they have simple critical points with only two (finite) critical values. Those properties uniquely determine the named polynomials modulo affine transformations of dependent and independent variables. A similar property of Zolotarev fractions: simple critical points and only four critical values generates already many classes of rational functions modulo projective transformations of their dependent and independent variables. They are listed in this note.

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Andrei Bogatyrev. 2015-11-17. How many Zolotarev fractions are there?. https://doi.org/10.1007/s00365-017-9366-6

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