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Zbl 1234.30027
Chen, Zong-Xuan
On value distribution of difference polynomials of meromorphic functions. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 239853, 9 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Hayman proved that if $f(z)$ is a transcendental entire function, $n\geq 3$ is an integer and $a\ne 0$ is a constant, then $f'(z)-af(z)^n$ assumes all finite values infinitely often. The author proves the difference counterpart of Hayman's result in which $f'(z)$ is replaced by $f(z+c)-f(z)$, $f(z)$ is not of period $c$, with an additional assumption that $f(z)$ is an entire function of finite order. A simple example shows that the result is not true for all entire functions. The author also obtains some results for the case $n=2.$
[Alexander Ulanovskii (Stavanger)]

MSC 2000:: *30D35 Distribution of values (one complex variable)
30D20 General theory of entire functions

Keywords: entire function; value distribution; difference polynomials of entire functions

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