Some extensions of the four values theorem of Nevanlinna-Gundersen

Abstract

Nevanlinna showed that two distinct non-constant meromorphic functions on C must be linked by a Möbius transformation if they have the same inverse images counted with multiplicities for four distinct values. Later on, Gundersen generalized the result of Nevanlinna to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with counting multiplicities. In this paper, we will extend the results of Nevanlinna-Gundersen to the case of two holomorphic mappings into Pⁿ(C) sharing (n + 1) hyperplanes ignoring multiplicity and other (n + 1) hyperplanes with multiplicities counted to level 2 or (n + 1).