关于亚纯函数的值分布和正规族的几个结果

发布时间：2018-05-19 20:43

本文选题：亚纯函数 + 微分多项式　；参考：《南京师范大学》2015年硕士论文

【摘要】：正规族理论是复分析中的重要课题,函数值分布是研究正规定则的有力工具.本文主要研究了亚纯函数正规族和值分布方面,得到了一些好的结论.论文安排如下：前言里,我们简单叙述了值分布论与亚纯函数正规族的发展脉络及此领域的某些研究成果.第一章,我们给了这篇文章中所需的基础理论：值分布论与正规族的基本概念,记号及基本结果.第二章,我们运用正规族理论研究了一类关于微分多项式的亚纯函数的值分布,使得结果一定程度上改进了徐焱和仇惠玲在[16]中的结果.第三章,我们研究并得到了一个关于分担函数的正规定则.推广戚建明和朱泰英[11],邹海斌[22]等人的相关结果.第四章,我们研究并得到了一类关于微分多项式的正规定则,推广和改进了兰富祥[6]等人的相关结果.
[Abstract]:The theory of normal family is an important subject in complex analysis, and the distribution of function values is a powerful tool for studying normal rules. In this paper, we mainly study the normal family and value distribution of meromorphic functions, and get some good results. The thesis is arranged as follows: in the preface, we briefly describe the development of the theory of value distribution and the normal family of meromorphic functions and some research results in this field. In the first chapter, we give the necessary basic theories in this paper: value distribution theory and the basic concepts, symbols and results of normal families. In the second chapter, we use the normal family theory to study the value distribution of a class of meromorphic functions on differential polynomials, which improves the results of Xu Yan and Qiu Huiling in [16] to some extent. In the third chapter, we study and obtain a normal rule about shared function. Promote the related results of Qi Jianming and Zhu Taiying [11], Zou Haibin [22], et al. In chapter 4, we study and obtain a class of normal rules on differential polynomials, which generalize and improve the related results of Lan Fuxiang [6] and others.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.52

【参考文献】