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A uniqueness result on some differential polynomials sharing 1-points. (English) Zbl 1152.30023

In the paper the uniqueness of meromorphic functions \(f\) and \(g\) is considered when \(f^{n}(f - 1)f'\) and \(g^{n}(g - 1)g'\) share only simple and double \(1\)-points. Using ramification index for poles, the author is able to reduce the lower bound of the power \(n\) of \(f\) and \(g\) than those obtained by others.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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