Zhang, Jilong; Gao, Zongsheng; Li, Sheng Distribution of zeros and shared values of difference operators. (English) Zbl 1236.39021 Ann. Pol. Math. 102, No. 3, 213-221 (2011). 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 \(\Delta^k_c f\neq 0\) for \(n\geq 2\), and \(a\) is a small function with respect to \(f\), then \(f^n\Delta^k_c f\) equals \(a\,(\neq 0,\infty)\) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved. Reviewer: Miloš Čanak (Beograd) Cited in 2 ReviewsCited in 3 Documents MSC: 39A70 Difference operators 39A05 General theory of difference equations 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory Keywords:meromorphic function; difference; shared value PDFBibTeX XMLCite \textit{J. Zhang} et al., Ann. Pol. Math. 102, No. 3, 213--221 (2011; Zbl 1236.39021) Full Text: DOI