A unicity theorem for meromorphic functions (Q5902238)

The paper under review deals with the uniqueness problem for meromorphic functions. The authors obtain the following theorem: Let \(f(z)\) and \(g(z)\) be two non-constant meromorphic functions the zeros and poles of which are of multiplicities at least \(s\) (\(\in N_+\)). Let \(n\geq2\) be an integer satisfying \((n+1)s>12\). If \(f^nf'\) and \(g^ng'\) share the value 1 \(CM\), then either \(f=dg\), for some \((n+1)^{th}\) root of unity \(d\), or \(f(z)=c_1e^{cz}\) and \(g(z)=c_2e^{-cz}\), where \(c,c_1,c_2\) satisfy \((c_1c_2)^{n+1}c^2=-1\). This theorem is similar to results of C. C. Yang and X. Hua.