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On value distribution of difference polynomials of meromorphic functions. (English) Zbl 1234.30027
Hayman proved that if f(z) is a transcendental entire function, n3 is an integer and a0 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·

30D35Distribution of values (one complex variable); Nevanlinna theory
30D20General theory of entire functions