Meromorphic Functions Sharing a Small Function

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...

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Bibliographic Details
Main Authors: Songmin Wang, Zongsheng Gao
Format: Article
Language:English
Published: Wiley 2007-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2007/60718
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Summary: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.
ISSN:1085-3375
1687-0409