an:00205781
Zbl 0777.30017
Wang, Yaofei
On Mues conjecture and Picard values
EN
Sci. China, Ser. A 36, No. 1, 28-35 (1993).
00012977
1993
j
30D35
Mues conjecture; Picard values
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 \textit{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.
W.H.Fuchs (Ithaca)
Zbl 0115.062