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arXiv · 2610.40202

On a class of meromorphic functions with three singular values

Alexandre Eremenko
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Abstract

We give a parametrization of the class of real meromorphic functions in the plane for which the preimage of $\{0,1,\infty\}$ is contained in the real line, and all singular values belong to $\{0,1,\infty\}$. As corollaries, we obtain a new parabolic type criterion and prove that all such functions are limits of rational functions of the same class.

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Alexandre Eremenko. 2026-10-29. On a class of meromorphic functions with three singular values. https://arxiv.org/abs/2610.40202

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