On order of homogeneous differential polynomials (Q1072676)

This article proves the following theorem: Let f(z) be a transcendental meromorphic function and let \(\phi\) (z) be a non-vanishing homogeneous differential polynomial such that for non-vanishing homogeneous differential polynomial such that for each term, the exponent of f(z) is \(\geq 1\). Then f(z) and \(\phi\) (z) have the same order of growth. This theorem generalizes a theorem due to \textit{L. R. Sons} [Math. Z. 111, 53- 68 (1969; Zbl 0176.372)].