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A note on the value distribution of \(f^2(f^\prime)^n\) for \(n\geq 2\). (English) Zbl 1341.30029

Summary: Let \(f\) be a transcendental meromorphic function in the complex plane \(\mathbb{C}\), and \(a\) be a nonzero constant. We give a quantitative estimate of the characteristic function \(T(r,f)\) in terms of \(N\big(r,1/(f^2(f^\prime)^n-a)\big)\), which states as following inequality, for positive integers \(n\geq 2\), \[ T(r,f)\leq \left(3+\frac{6}{n-1}\right)N\left(r,\frac{1}{af^2(f^{\prime})^n-1}\right)+S(r,f). \]

MSC:

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