[1]胡雅倩,徐 焱.亚纯函数正规族的一点注记[J].南京师大学报(自然科学版),2020,43(04):6-8.[doi:10.3969/j.issn.1001-4616.2020.04.002]
　Hu Yaqian,Xu Yan.A Note on the Normal Family of Meromorphic Functions[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(04):6-8.[doi:10.3969/j.issn.1001-4616.2020.04.002]
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亚纯函数正规族的一点注记()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年04期
页码:
6-8
栏目:
·数学·
出版日期:
2020-12-30

文章信息/Info

Title:
A Note on the Normal Family of Meromorphic Functions
文章编号:
1001-4616(2020)04-0006-03
作者:
胡雅倩; 徐 焱
南京师范大学数学科学学院,江苏 南京 210023
Author(s):
Hu Yaqian; Xu Yan
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
关键词:
Hayman猜测; 亚纯函数; 正规族
Keywords:
Hayman’s conjecture; meromorphic function; normal family
分类号:
O174.52
DOI:
10.3969/j.issn.1001-4616.2020.04.002
文献标志码:
A
摘要:
本文研究了亚纯函数正规定则,得到下面结果. 设k≥4是正整数,F为区域D内的一族亚纯函数,f∈F,a(z)(0,∞)是D内亚纯函数,且满足当a(z)=0时, f(z)≠∞; 当a(z)=∞时, f(z)≠0. 若f’(z)-a(z)fk(z)≠0,则F在D内正规.
Abstract:
In this paper,we discuss the normality concerning omitted meromorphic function and get the following results. Let F be a family of meromorphic functions on a domain D,k≥4 be a positive integer,and let a(z)(0,∞)be a meromorphic function on D which satisfies f(z)≠∞ whenever a(z)=0 and satisfies f(z)≠0 whenever a(z)=∞. If for any f∈F,f’(z)-a(z)fk(z)≠0,then F is normal on D.

参考文献/References:

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[2]LI X J. Proof of Hayman’s conjecture on normal families[J]. Science in China,1985(6):38-45.
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[4]CHEN H H,FANG M L. The value distribution of . Science in China,1995,38(7):23-32.
[5]YANG J H,YANG Q,PANG X C. A normal criterion concerning omitted holomorphic function[J]. Acta mathematics sinica,2019,35(12):1972-1978.
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备注/Memo

备注/Memo:
收稿日期:2019-12-30.
基金项目:国家自然科学基金项目(11471163).
通讯作者:胡雅倩,硕士研究生,研究方向:复分析. E-mail:1255663084@qq.com
更新日期/Last Update: 2020-11-15