A unicity theorem for meromorphic mappings (Q2705808)

The well-known Nevanlinna four-value theorem states that if two meromorphic functions \(f\) and \(g\) in the complex plane \(\mathbb{C}\) share four distinct values by counting multiplicities, then there exists a Möbius transformation \(L\) such that \(f=L(g)\). The author extended the theorem to two meromorphic mappings \(f\) and \(g\) from \(\mathbb{C}^n\) into \(\mathbb{P}^m\) with \(2(m+1)\) moving targets in general position. In particular, when \(m=1\) the main theorem of the author says that if two meromorphic functions \(f\) and \(g\) in \(\mathbb{C}^n\) share four distinct small functions in \(\mathbb{C}^n\) (with respect to \(f\)) by counting multiplicities, then there exist four small functions \(a,b,c,d\) in \(\mathbb{C}^n\) (with respect to \(f\)) with \(ad-bc\not\equiv 0\) such that NEWLINE\[NEWLINEf=\frac{ag+b}{cg+d}.NEWLINE\]NEWLINE Further, if \(n=1\), this result was obtained by \textit{M. Shirosaki} [Tôhoku Math. J., II. Ser. 45, No. 4, 491-497 (1993; Zbl 0802.30026)].