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http://dx.doi.org/10.4134/BKMS.2010.47.2.319

MEROMORPHIC FUNCTIONS SHARING A NONZERO POLYNOMIAL CM  

Li, Xiao-Min (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA)
Gao, Ling (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 319-339 More about this Journal
Abstract
In this paper, we prove that if $f^nf and $g^ng share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.
Keywords
meromorphic functions; shared values; differential polynomials; uniqueness theorems;
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