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Bulletin of the London Mathematical Society Advance Access originally published online on January 6, 2009
Bulletin of the London Mathematical Society 2009 41(1):63-71; doi:10.1112/blms/bdn103
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© 2009 London Mathematical Society

Normal families and omitted functions II

Guoming Zhang

Department of Mathematics
East China Normal University
Shanghai 200062
P.R. China
zhangguoming1985@21cn.com

Xuecheng Pang

Department of Mathematics
East China Normal University
Shanghai 200062
P. R. China
xcpang@euler.math.ecnu.edu.cn

Lawrence Zalcman

Department of Mathematics
Bar-Ilan University
52900 Ramat-Gan
Israel

Received 25 April 2008. Revision received 22 July 2008.

Let k ≥ 2 be an integer and let F be a family of functions meromorphic on a domain D in C, all of whose poles are multiple and whose zeros all have multiplicity at least k + 1. Let h be a function meromorphic on D, h nequiv 0, {infty}. Suppose that for each f isin F, f(k)(z) != h(z) for z isin D. Then F is a normal family on D.

2000 Mathematics Subject Classification 30D45.

X. P. was supported by the NSSF of China Grant No. 10671067, and L. Z. was supported by the German–Israeli Foundation for Scientific Research and Development Grant G-809-234.6/2003 and Israel Science Foundation Grant 395/07.


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