Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity
By J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, Jilong Zhang. 2009
228 citations recorded by the source corpus.
Abstract This research is a continuation of a recent paper due to the first four authors. Shared value problems related to a meromorphic function f ( z ) and its shift f ( z + c ) , where c ∈ C , are studied. It is shown, for instance, that if f ( z ) is of finite order and shares two values CM and one value IM with its shift f ( z + c ) , then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions. The research findings also include an analogue for shifts of a well-known conjecture by Bruck concerning the value sharing of an entire function f with its derivative f ′ .
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0eb013ed3645bc506f1635f3b4a59e7747ed25a9
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- On Sharing Values of Meromorphic Functions and Their Differences (2013, background): “In [9], Heittokangas et al.”