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A uniqueness theorem for meromorphic functions whose \(N\)-th derivatives share the same 1-points. (English) Zbl 0799.30019
The authors continue their work on uniqueness theorem arising from common point properties. Their main result here is the theorem: If \(f\) and \(g\) are two meromorphic functions with \(\theta(\infty,f)= \theta(\infty,g)= 1\) and if \(f^{(n)}= 1\) if and only if \(g^{(n)}= 1\) and \(\delta(0,f)+ \delta(0,g)> 1\), then either \(f\equiv q\) or \(f^{(n)} g^{(n)}\equiv 1\).

MSC:
30D30 Meromorphic functions of one complex variable, general theory
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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