Meromorphic functions that share three sets
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 \(s^n=1\).
scientific article; zbMATH DE number 1057147
scientific article