Computational Methods and Function Theory 1 (2001), No. 2, 457--478
Copyright Heldermann Verlag 2001
Jürgen Grahl
grahl@mathematik.uni-wuerzburg.de, Universität Würzburg, Mathematisches Institut, Am Hubland, 97074 Würzburg, Germany.
We show that if an entire function $f$ satisfies $$ af^n(z)+f^{(k)}(z)+P[f](z)\ne 0 $$ for all $z\in\mathbb{C}$, for some $n\ge 2$, $k\ge 1$, $a\ne 0$, and with $P$ a differential polynomial of a certain form, then $f$ must be a constant. We also prove the corresponding normality criterion where the coefficients are meromorphic functions. This generalizes results of Hayman \cite{haym2}, Drasin \cite{drasin} and Chen and Hua \cite{chenhua}.
Keywords: Normality, differential polynomials, Zalcman's Lemma, Bloch's Principle, Tumura-Clunie Theorem.
MSC 2000: 30D35, 30D45.
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