[1]黄小杰,刘芝秀,李运通.分担集合的正规亚纯函数[J].南京师范大学学报(自然科学版),2018,41(04):12.[doi:10.3969/j.issn.1001-4616.2018.04.003]
　Huang Xiaojie,Liu Zhixiu,Li Yuntong.Normal Function Related to Shared Sets[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(04):12.[doi:10.3969/j.issn.1001-4616.2018.04.003]
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分担集合的正规亚纯函数()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第41卷
期数:
2018年04期
页码:
12
栏目:
·数学与计算机科学·
出版日期:
2018-12-31

文章信息/Info

Title:
Normal Function Related to Shared Sets
文章编号:
1001-4616(2018)04-0012-07
作者:
黄小杰1; 2; 刘芝秀1; 李运通3
(1.南昌工程学院理学院,江西 南昌 330099)(2.复旦大学数学科学学院,上海 杨浦 200433)(3.陕西铁路职业技术学院,陕西 渭南 714000)
Author(s):
Huang Xiaojie1; 2; Liu Zhixiu1; Li Yuntong3
(1.Department of Science,Nanchang Institute of Technology,Nanchang 330099,China)(2.School of Mathematic Sciences,Fudan University,Shanghai 200433,China)(3.Shanxi Railway Institute,Weinan 714000,China)
关键词:
正规函数; 正规族; 分担集合
Keywords:
normal function; normal family; shared set
分类号:
O174.5
DOI:
10.3969/j.issn.1001-4616.2018.04.003
文献标志码:
A
摘要:
研究了涉及函数与其高阶导数分担集合的亚纯函数正规条件,利用Lohwater-Pommerenke定理和 Zalcman-Pang引理以及Nevanlinna理论证明了如下结论,设S1={a1,a2,a3}和S2={b1,b2}是由互异有限复数构成的集合,k≥2是一个正整数,f(z)是单位圆Δ内的亚纯函数,如果f(z)-ai的零点重数都至少为k,i=1,2,3,且{z∈Δ|f(z)∈S1}={z∈Δ|f(k)(z)∈S2},那么f(z)是Δ上的正规函数.
Abstract:
This paper studies the normal conditions of meromorphic function relating to sharing sets by the function and its higher derivatives. By use of Lohwater-Pommerenke’s theorem and Zalcman-Pang’s lemma as well as Nevanlinna theory,it proves that let S1={a1,a2,a3}and S2={b1,b2}be two sets consisting of different finite complex numbers,k≥2 be a positive integer number,if f(z) be a meromorphic function on unit circle domain Δ such that the zeros of f(z)-ai have multiplicity at least k,i=1,2,3 and {z∈Δ|f(z)∈S1}={z∈Δ|f(k)(z)∈S2},then f(z)is a normal function on domain Δ.

参考文献/References:

[1] STEINME T Z N. Nevanlinna theory,normal family,and algebraic differential equation[M]. Berlin:Springer Press,2017.
[2]HAYMAN W K,STORVICK D A. On normal functions[J]. Bull London Math Soc,1971,3:193-194.
[3]GU Y X. A normal criterion of families of meromorphic function[J]. Chinese science,1979(S1):269-276.
[4]LIU X J,PANG X C. Shared values and normal families[J]. Acta Math Sinica,2007,50(2):409-412.
[5]CHANG J M,WANG Y F. Shared values,Picard values and normality[J]. Tohoku Math J,2011,63:149-162.
[6]XU Y,QIU H L. Normal functions and shared sets[J]. Filomat,2016,30(2):287-292.
[7]LOHWATER A J,POMMERENKE CH. On normal meromorphic functions[J]. Ann Acad Sci Fenn Ser A I Math,1973,550:12.
[8]PANG X C,ZALCMAN L. Normal families and shared values[J]. Bull London Math Soc,2000,32:325-331.
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[10]YANG L. Value distribution theory[M]. Berlin:Springer-Verlag and Science Press,1993.

相似文献/References:

[1]胡雅倩,徐 焱.亚纯函数正规族的一点注记[J].南京师范大学学报(自然科学版),2020,43(04):6.[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.[doi:10.3969/j.issn.1001-4616.2020.04.002]

备注/Memo

备注/Memo:
收稿日期:2017-11-19.
基金项目:国家自然科学基金(11671091、11771090)、上海市自然科学基金(17ZR1402900)、陕西省教育厅专项基金(17JK0170)、江西省教育厅科技项目(GJJ180944).
通讯联系人:黄小杰,博士,讲师,研究方向:复分析. E-mail:xjhuang14@fudan.edu.cn
更新日期/Last Update: 2018-12-30