Meromorphic Functions Sharing a Small Function

Songmin Wang; Zongsheng Gao
January 2007
Abstract & Applied Analysis;2007, p1
Academic Journal
We will study meromorphic functions that share a small function, and prove the following result: let f (z) and g(z) be two transcendental meromorphic functions in the complex plane and let n ≥ 11 be a positive integer. Assume that a(z)(≢ 0) is a common small function with respect to f (z) and g(z). If fn f' and gng' share a(z) CM, then either fn(z) f' (z)gn(z)g' (z) ≡ a²(z), or f (z) ≡ tg(z) for a constant satisfying tn+1 = 1. As applications, we give several examples.


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