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Hindawi Publishing Corporation Advances in Difference Equations Volume 2011, Article ID 234215, 12

Hindawi Publishing Corporation Advances in Difference Equations Volume 2011, Article ID 234215, 12 pages doi:10.1155/2011/234215 Research Article Value Distributions and Uniqueness of Difference Polynomials Kai Liu, Xinling Liu, and TingBin Cao Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, China Correspondence should be addressed to Kai Liu, liukai418@126.com Received 21 January 2011; Accepted 7 March 2011 Academic Editor: Ethiraju Thandapani Copyright q 2011 Kai Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the zeros distributions of. | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 234215 12 pages doi 10.1155 2011 234215 Research Article Value Distributions and Uniqueness of Difference Polynomials Kai Liu Xinling Liu and TingBin Cao Department of Mathematics Nanchang University Nanchang Jiangxi 330031 China Correspondence should be addressed to Kai Liu liukai418@126.com Received 21 January 2011 Accepted 7 March 2011 Academic Editor Ethiraju Thandapani Copyright 2011 Kai Liu et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We investigate the zeros distributions of difference polynomials of meromorphic functions which can be viewed as the Hayman conjecture as introduced by Hayman 1967 for difference. And we also study the uniqueness of difference polynomials of meromorphic functions sharing a common value and obtain uniqueness theorems for difference. 1. Introduction A meromorphic function means meromorphic in the whole complex plane. Given a meromor-phic function f recall that a 0 TO is a small function with respect to f if T fr a S r f where S r f is used to denote any quantity satisfying S r f o T r f as r TO outside a possible exceptional set of finite logarithmic measure. We use notations p f 1 1 f to denote the order of growth of f and the exponent of convergence of the poles of f respectively We say that meromorphic functions f and g share a finite value a IM ignoring multiplicities when f - a and g - a have the same zeros. If f - a and g - a have the same zeros with the same multiplicities then we say that f and g share the value a CM counting multiplicities . We assume that the reader is familiar with standard notations and fundamental results of Nevanlinna Theory 1-3 . As we all know that a finite value a is called the Picard exception value of f if f - a has no zeros. The Picard .