Meromorphic Functions Sharing a Small Function
Songmin Wang and Zongsheng Gao
Source: Abstr. Appl. Anal. Volume 2007 (2007), 6 pages.
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 $n \ge 11$ be a positive integer. Assume that $a(z) (\nequiv 0)$ is a common small function with respect to $f(z)$ and $g(z)$. If $f^n f^\prime$ and $g^n g^\prime$ share $a(z)$ CM, then either $f^n (z) f^\prime (z)g^n (z) g^\prime (z) = a^2 (z)$, or $f(z) \equiv tg (z)$ for a constant satisfying $t^{n+1} =1 $. As applications, we give several examples.
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Permanent link to this document: http://projecteuclid.org/euclid.aaa/1183666875
Digital Object Identifier: doi:10.1155/2007/60718
Abstract and Applied Analysis
