Picard sets and value distribution for differential polynomials (Q1323914)

In the present paper the value distribution of differential polynomials is studied. The main result is: Let \(f\) be an entire function, \(Q(f)\) a differential polynomial, and \(F= f^ n Q(f)\) with \(n\geq 3\). Let \(M= \{ \lambda_ k\}\), \(k\in \mathbb{N}\), be a point set in \(\mathbb{C}\) with \(| \lambda_{k+1} /\lambda_ k |> q>1\). Then for any polynomial \(R(z) \not\equiv 0\) the difference \(F'- R(z)\) has infinitely many zeros in \(\mathbb{C}\setminus M\). There are relations to theorems of Anderson et al., Tumura, Clunie, Milloux and Hayman.