On Bloch's "Principle of topological continuity''
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917856048840704 |
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| author | Bergweiler, Walter Eremenko, Alexandre |
| author_facet | Bergweiler, Walter Eremenko, Alexandre |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14749 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Bloch's "Principle of topological continuity'' Bergweiler, Walter Eremenko, Alexandre Complex Variables 30D30, 30D35, 30D45 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. |
| title | On Bloch's "Principle of topological continuity'' |
| topic | Complex Variables 30D30, 30D35, 30D45 |
| url | https://arxiv.org/abs/2309.14749 |