Unicity theorems for meromorphic functions
The authors proved the following result: Take a positive integer \(n\). Let \(f\) and \(g\) be nonconstant meromorphic functions in \(\mathbb{C}\) such that Nevanlinna defects of \(f\) and \(g\) for \(0\) and \(\infty\) satisfy NEWLINE\[NEWLINE\delta(0,f)+\delta(0,g)>2-\frac{1}{2(n+1)}NEWLINE\]NEWLINE and NEWLINE\[NEWLINE\Theta(\infty,f)=\Theta(\infty,g)=1.NEWLINE\]NEWLINE If \(a\;(\not\equiv 0),b\;(\not\equiv 0)\) are small meromorphic functions of \(f\) and \(g\) such that \(f^{(n)}-a\) and \(g^{(n)}-b\) share \(0\) CM, then either \(f^{(n)}g^{(n)}=ab\) or \(f^{(n)}/a=g^{(n)}/b\). Many similar results can be found in Yi and Yang's book [Science Press, China, 1995].
scientific article; zbMATH DE number 1640445