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On a class of meromorphic functions with three singular values
Abstract
We give a parametrization of the class of real meromorphic functions in the plane for which the preimage of {0,1,∞} is contained in the real line, and all singular values belong to {0,1,∞}. 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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BibTeX
@misc{eremenko2026class,
title = {{On a class of meromorphic functions with three singular values}},
author = {Alexandre Eremenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40202},
eprint = {2610.40202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40202},
}
RIS
TY - UNPB
TI - On a class of meromorphic functions with three singular values
AU - Alexandre Eremenko
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40202
UR - https://arxiv.org/abs/2610.40202
AB - We give a parametrization of the class of real meromorphic functions in the plane for which the preimage of {0,1,∞} is contained in the real line, and all singular values belong to {0,1,∞}. As corollaries, we obtain a new parabolic type criterion and prove that all such functions are limits of rational functions of the same class.
ER -