A note on normality and shared values

J. Aust. Math. Soc. 76 (2004), 141-150

A note on normality and shared values

Mingliang Fang
Department of Mathematics
Nanjing Normal University
Nanjing 210097
P. R. China
mlfang@pine.njnu.edu.cn

and

Lawrence Zalcman
Department of Mathematics and Statistics
Bar-Ilan University
52900 Ramat-Gan
Israel
zalcman@macs.biu.ac.il

Abstract

Let

be a positive integer and

a nonzero constant. Suppose that $\mathcal{F}$ is a family of meromorphic functions in a domain

. If each function $f\in \mathcal{F}$ has only zeros of multiplicity at least

and for any two functions $f, g\in \mathcal{F}$ ,

and

and $f^{(k)}$ and $g^{(k)}$ share

, then $\mathcal{F}$ is normal in

. The case $f\not= 0$ , $f^{(k)}\not= b$ is a celebrated result of Gu.