An extension of unicity theorem for meromorphic functions (Q1319190)

If \(f,g : {\mathcal C} \to \widehat {\mathcal C}\) are two meromorphic functions and if \(a_ 1, a_ 2, \dots, a_ 5\) are five distinct meromorphic functions satisfying \(T(r,a_ j) = oT(r,f)\) \((r \to \infty)\), then \(f \equiv g\), if \(f - a_ j\) and \(g - a_ j\) have the same zeros (taking account of multiplicities) for \(j = 1, \dots,5\). In the case of constant \(a\) this was proved by R. Nevanlinna without any restriction on the multiplicities of the zeros.