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On unavoidable families of meromorphic functions

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  18 November 2021

Thierry Meyrath
Thierry Meyrath*
Affiliation:
Department of Mathematics, University of Luxembourg, 6, Avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg
*
e-mail: [email protected]
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Abstract

We prove several results on unavoidable families of meromorphic functions. For instance, we give new examples of families of cardinality 3 that are unavoidable with respect to the set of meromorphic functions on $\mathbb C$ . We further obtain families consisting of less than three functions that are unavoidable with respect to certain subsets of meromorphic functions. In the other direction, we show that for every meromorphic function f, there exists an entire function that avoids f on $\mathbb C$ .

Keywords

Unavoidable familieszero–one setsNevanlinna Theory

MSC classification

Primary: 30D30: Meromorphic functions, general theory 30D35: Distribution of values, Nevanlinna theory 30D20: Entire functions, general theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 114 - 123
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Copyright
© Canadian Mathematical Society, 2021

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