Meromorphic functions that share three sets. (English) Zbl 0882.30019

Yi, Hong-Xun

Kodai Math. J. 20, No. 1, 22-32 (1997).

Let \(n\) be a positive integer, and let \(w= \exp (2\pi i/n)\). Let \(S_1= \{1,w,w^2, \dots, w^{n-1}\}\), \(S_2 =\{0\}\), and \(S_3= \{\infty\}\). The author proves six theorems which are improvements or supplements to known results. A typical theorem assumes \(f\) and \(g\) are nonconstant meromorphic functions in the plane which share sets \(S_1\) and \(S_3\), counting multiplicity, and \(S_2\) ignoring multiplicity and proves that if \(n\geq 2\), then \(f=tg\) where \(t^n=1\) or \(f\cdot g=s\) where \(s^n=1\).

Reviewer: L.R.Sons (DeKalb)

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D30	Meromorphic functions of one complex variable (general theory)
30D20	Entire functions of one complex variable (general theory)

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