Meromorphic Functions Sharing a Small Function

Songmin Wang and Zongsheng Gao

Abstract and Applied Analysis, 2007, vol. 2007, issue 1

Abstract: 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 fnf′ 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.

Date: 2007
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https://doi.org/10.1155/2007/60718

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:060718

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