Über den Verzweigungsindex bei ganzen Funktionen

Abstract

Recently the author proved ([3]) for entire functions f(z) and any complex a: Each set of n a-points of f(z), which are near (with respect to the order of f(z)) to each another can be considered in view of the second fundamental theorem of Nevanlinna as an a-point of at least multiplicity two if n>1. In the present paper it will be proved: Each set of n a-points of f(z), which are very near (with respect to the order of f(z)) to each another can be considered in view of the second fundamental theorem of Nevanlinna as an a-point of at least multiplicity n−1.