Meromorphic functions that share one or two values. (English) Zbl 0841.30027

Yi, Hong-Xun

Complex Variables, Theory Appl. 28, No. 1, 1-11 (1995).

In this paper, the author continues his researches on the relationships of two nonconstant meromorphic functions \(f,g\) that share one or two values \(CM\). It is shown that if \(f\) and \(g\) share \(ICM\) satisfying the condition: \[ \lim_{r \in I} \sup N_2 (r, 1/f) + N_2 (1,f) + N_2 (r, 1/g) + N_2 (r, g)/T(r) < 1, \] where \(T(r) = \max \{T(r, f), T(r, g)\}\) and \(I\) is a set of \(r\) values of infinite linear measure, then \(f \equiv g\) or \(fg \equiv 1\). With slight variation of the above condition, the same conclusions hold when \(f\) and \(g\) share \(1, \infty \subset M\).

Reviewer: C.-C.Yang (Kowloon)

MSC:

30D35

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

Keywords:

Möbius transformation; lacunary; share value