亚纯函数关于单叶离散值的正规定理

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1598-1605.

亚纯函数关于单叶离散值的正规定理

郭晓晶¹(),柴富杰²(),孙道椿^3,*()

¹ 广东培正学院数据科学与计算机学院广州 510830
² 广东金融学院金融数学与统计学院广州 510521
³ 华南师范大学数学科学学院广州 510631

收稿日期:2020-06-11 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 孙道椿 E-mail:betty0104@sina.com;chaifujie@sina.com;1457330943@qq.com
作者简介:郭晓晶, E-mail: betty0104@sina.com|柴富杰, E-mail: chaifujie@sina.com
基金资助:
国家自然科学基金(11501127);广州民航学院基金(18X0428)

Normal Family Theorems for Meromorphic Functions with Discrete Values of One Leaf

Xiaojing Guo¹(),Fujie Chai²(),Daochun Sun^3,*()

¹ School of Data Science and Computer Science, Guangdong Peizheng College, Guangzhou 510830
² School of Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521
³ School of Mathematics Science, South China Normal University, Guangzhou 510631

Received:2020-06-11 Online:2021-12-26 Published:2021-12-02
Contact: Daochun Sun E-mail:betty0104@sina.com;chaifujie@sina.com;1457330943@qq.com
Supported by:
the NSFC(11501127);the Guangzhou Civil Aviation College(18X0428)

摘要/Abstract

摘要：

该文应用Ahlfors覆盖曲面理论研究了涉及离散值的亚纯函数的正规定理.首先定义了亚纯函数的单叶离散值，然后深入考察了Ahlfors关于岛的不等式，得到两个关于岛的精密不等式.最后应用所得到的不等式研究了亚纯函数的离散值和正规族，得到了一个涉及单叶岛的正规定理和一个涉及单叶离散值的正规定理，这些定理推广了著名的Ahlfors五岛定理与Nevanlinna五单值定理.

关键词: 亚纯函数, 正规族, 覆盖曲面, 岛, 单叶离散值

Abstract:

In this paper, the normal theorems of meromorphic functions involving discrete values are studied by using the theory of Ahlfors covering surfaces. Firstly, the discrete values with one leaf of meromorphic functions are defined, then the inequalities about islands are investigated and two precise inequalities about islands are obtained. Finally, the inequalities are used to study the discrete values and the normal family of meromorphic functions, then a normal theorem involving a monophyletic island and a normal theorem involving discrete values of one leaf are obtained. All these theorems promote the famous Ahlfors' five islands theorem and five single valued theorem of Nevanlinna.

Key words: Meromorphic functions, Normal family, Covering surface, Island, Discrete values of one Leaf

中图分类号:

O174.52

郭晓晶,柴富杰,孙道椿. 亚纯函数关于单叶离散值的正规定理[J]. 数学物理学报, 2021, 41(6): 1598-1605.

Xiaojing Guo,Fujie Chai,Daochun Sun. Normal Family Theorems for Meromorphic Functions with Discrete Values of One Leaf[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1598-1605.

参考文献 10

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