Meromorphic function without multiple values in the punctured plane.

Arturo Fernández

The study of meromorphic functions in the plane without multiple values was initiated by F.Nevanlinna. His method was based on the work of E.Hille on complex differential equations. We shall extend F.Nevanlinna's investigations to the wider setting of meromorphic functions in the punctured plane. The frame of this study is the value distribution theory of meromophic functions. Here we shall make use of the extension of Nevanlinna Theory to annuli due to K.H.Khrystiyanin and A.A.Kondratyuk and R.Korhonen.