On the uniqueness of meromorphic functions that share three or two finite sets on annuli (Q692362)

The authors consider the uniqueness of meromorphic functions that share three or two finite sets on annuli and obtain the following result: Let \(f\) and \(g\) be two admissible meromorphic function in an annulus \(\mathbb{A}\). Put \(S_1=\{0\}, S_2=\{\infty\}\) and \(S_3=\{w:P(w)=0\}\), where \[ P(w)=aw^n-n(n-1)w^2+2n(n-2)bw-(n-1)(n-2)b^2, \] \(n\geq 5\) is an integer, and \(a\) and \(b\) are two nonzero complex numbers satisfying \(ab^{n-2}\neq 1,2\). If \(\overline{E}(S_2,f)=\overline{E}(S_2,g)\) and \(E(S_j,f)=E(S_j,g)\) for \(j=1,3\) then \(f(z)\equiv g(z)\).