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On dependence of meromorphic functions sharing some finite sets IM. (English) Zbl 1337.30044

In connection with Nevanlinna’s five-value theorem, the author shows that if \(n+1\) meromorphic functions \(f_1,\dots,f_{n+1}\) on \(\mathbb{C}\) sharing some finite sets IM (ignoring multiplicities), then there exists a Möbius transformation \(T\) such that \(T(f_1)+\cdots+T(f_{n+1})=0\).

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D99 Entire and meromorphic functions of one complex variable, and related topics
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References:

[1] W. K. Hayman, Meromorphic functions , Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. · Zbl 0115.06203
[2] R. Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), no. 3-4, 367-391. · JFM 52.0323.03
[3] M. Shirosaki, On meromorphic functions sharing five one-point or two-point sets IM, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 1, 6-9. · Zbl 1263.11062
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