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On Mues conjecture and Picard values. (English) Zbl 0777.30017
Let \(f\) be a transcendental meromorphic function. Then
(i) \(\sum_{a\in\mathbb{C}}\delta(a,f^{(k)})\leq 1\) holds for all \(k\geq 0\) with at most four exceptions.
(ii) For \(n\geq 3\), \(k\geq 0\) \((f^ n)^{(k)}\) assumes every complex value other than 0 infinitely often. Improvements of W. K. Hayman’s bound on \(T(r,f)\) in terms of \(N(r,1/f)\) and \(N(r,1/(f^{(k)}-1))\) [Meromorphic functions (1964; Zbl 0115.062)] are also given. These results are important improvement of previous work by many authors.
Reviewer: W.H.Fuchs (Ithaca)

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