Exceptional values of certain homogeneous differential polynomials (Q1281330)

\textit{W. K. Hayman} [Meromorphic functions (1964; Zbl 0115.62003)] showed that if \(f\) is a transcendental meromorphic function in the plane and \(m\) is a positive integer, then either \(f\) assumes every complex number or \(f^{(m)}\) assumes every complex number except possibly zero. In the paper under review the authors use techniques of W. Hayman and Lo Yang [\textit{L. Yang}, Acta. Math. Sin., New. Ser. 1, 181-192 (1985; Zbl 0603.30040)] to extend the above result by considering a homogeneous nonconstant differential polynomial \(\varphi\) in \(f\) and showing that either \(f\) assumes every finite value in \(\mathbb{C}\) infinitely often or \(\varphi\) assumes every finite nonzero value in \(\mathbb{C}\) infinitely often.