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SOME RESULTS ON VALUE DISTRIBUTION OF THE DIFFERENCE OPERATOR

In this article, we consider the uniqueness of the difference monomials fn(z)f(z + c). Suppose that f(z) and g(z) are transcendental meromorphic functions with finite order and Ek(1, f n(z)f(z + c)) = Ek(1, g n(z)g(z+ c)). Then we prove that if one of the following holds (i) n ≥ 14 and k ≥ 3, (ii) n ≥ 16 and k = 2, (iii) n ≥ 22 and k = 1, then f(z) ≡ t1g(z) or f(z)g(z) = t2, for some constants t1 and t2 that satisfy t 1 = 1 and t n+1 2 = 1. We generalize some previous results of Qi et. al.