Uniqueness of meromorphic functions and a question of C.C.Yang. (English) Zbl 0701.30025

Yi, Hong-Xun

Complex Variables, Theory Appl. 14, No. 1-4, 169-176 (1990).

The author proves the following Theorem: Let f and g be two nonconstant meromorphic functions in the plane, n be a nonnegative integer. Assume that \(f=0\rightleftarrows g=0\), \(f=\infty \rightleftarrows g=\infty\), \(f^{(n)}=1\rightleftarrows g^{(n)}=1\) and \[ \limsup_{r\to \infty}\frac{2N(r,1/f)+(n+z)\bar N(r,f)}{T(r,f)}<1. \] Then \(f\equiv g\) or \(f^{(n)}g(n)\equiv 1\).

Reviewer: Fred Gross

MSC:

30D35

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory