On a result of Terglane concerning uniqueness of meromorphic functions (Q1860734)

Let \(f\) and \(g\) be meromorphic in the plane. Denote by \(\overline{N}_0(r,a,f,g)\) the counting function of the common \(a\)-points of \(f\) and \(g\). \textit{N. Terglane} [Identitätssätze in \({\mathbb C}\) meromorpher Funktionen als Ergebnis von Werteteilung, Diplomarbeit, Aachen (1989)] proved that if \(\overline{N}_0(r,a,f,g)\not=S(r,f)\), if \(f\) and \(g\) share three other values \(b,c,d\) counting multiplicities, and if the cross ratio \((a,b,c,d)\) is different from -1, 2 and 1/2, then \(f\) is a linear transformation of \(g\). In this paper some related results are proved. For example it is shown that if \(f\) and \(g\) share \(b,c,d\) and if \(N_0(r,a_1,f,g)\not= S(r,f)\) and \(N_0(r,a_2,f,g)\not= S(r,f)\) for two further values \(a_1\) and \(a_2\), then \(f=g\).