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arXiv · 2309.14749

On Bloch's "Principle of topological continuity''

Walter Bergweiler·Alexandre Eremenko
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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 $1$ has a simple island over at least one of two given Jordan domains with disjoint closures.

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Walter Bergweiler, Alexandre Eremenko. 2023-09-26. On Bloch's "Principle of topological continuity''. https://doi.org/10.1007/s40315-024-00531-w

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