On Bloch's "Principle of topological continuity''
Complex Variables
2024-12-05 v1
Abstract
We discuss to what extent certain results about totally ramified values of entire and meromorphic functions remain valid if one relaxes the hypothesis that some value is totally ramified by assuming only that all islands over some Jordan domain are multiple. In particular, we prove a result suggested by Bloch which says that an entire function of order less than has a simple island over at least one of two given Jordan domains with disjoint closures.
Keywords
Cite
@article{arxiv.2309.14749,
title = {On Bloch's "Principle of topological continuity''},
author = {Walter Bergweiler and Alexandre Eremenko},
journal= {arXiv preprint arXiv:2309.14749},
year = {2024}
}
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32 pages