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Zbl 1236.39021
Zhang, Jilong; Gao, Zongsheng; Li, Sheng
Distribution of zeros and shared values of difference operators.
(English)
[J] Ann. Pol. Math. 102, No. 3, 213-221 (2011). ISSN 0066-2216; ISSN 1730-6272/e

The authors investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, they show that if $f$ is a transcendental meromorphic function of finite order with a small number of poles, $c$ is a non-zero complex constant such that $\Delta^k_c f\ne 0$ for $n\ge 2$, and $a$ is a small function with respect to $f$, then $f^n\Delta^k_c f$ equals $a\,(\ne 0,\infty)$ at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
MSC 2000:
*39A70 Difference operators
39A05 General theory of difference equations
30D35 Distribution of values (one complex variable)

Keywords: meromorphic function; difference; shared value

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