涉及微分多项式的亚纯函数正规性

发布时间：2018-05-03 11:11

  本文选题：亚纯函数 + 例外值　； 参考：《湖北大学》2015年硕士论文

【摘要】：1907年,P.Montel引进引进正规族的定义后,值分布理论得到了新的发展,其对值分布理论具有极其重要的意义；随后20世纪20年代,R.Nevanlinna第一基本定理,第二基本定理的引入带来了值分布理论的空前发展；而后Marty正规定则和Zalcman引理的发现后,为人们逆向寻找正规性带来了理论依据,为人们寻找正规性带来了新的思路与视野。随之以后,我国的一部分数学家也为值分布理论的发展作出了重大贡献,特别是熊庆来,杨乐,顾永兴,方明亮等人的研究处于国际前沿。基于正规性理论的探讨,本文主要分成五部分：第一部分是引言,分析值分布理论的发展与现状。第二部分主要介绍值分布理论的基础知识(Nevanlinna第一、第二基本定理,特征函数,对数导数基本引理等)和正规性理论的基本知识(按球面导数收敛、一致收敛,正规的概念,Marty正规定则,Zalcman引理以及Hurwitz定理)。第三部分由基本的Hayman司题出发,将条件由.f≠0,f(n)≠1减弱为fnf’≠1,再换成fn-f’≠1,另外条件n≥4也逐步变弱至n≥2,还有逐步将例外值向例外函数,函数列进行推进,逐步改善条件。第四部分同样由Hayman问题出发,不过与第二部分不同的是从分担值方面进行考虑,类似于第二部分逐步减弱条件,使得所得定理更加实用。第五部分结论与展望对当代值分布理论的探讨进行说明,并对相应的正规定则进行假设与推测。
[Abstract]:After P. Montel introduced the definition of normal family in 1907, the theory of value distribution got a new development, which is of great significance to the theory of value distribution, and the first fundamental theorem of R. Nevanlinna was introduced in the 1920s. The introduction of the second basic theorem brings an unprecedented development of the theory of value distribution, and after the discovery of the Marty normal rule and Zalcman Lemma, it brings a theoretical basis for people to search for normality in reverse, and a new train of thought and field of vision for people to search for normality. Subsequently, some mathematicians in China also made great contributions to the development of the theory of value distribution, especially Xiong Qinglai, Yang Le, Gu Yongxing, Fang Mingming, etc. Based on the discussion of normality theory, this paper is divided into five parts: the first part is the introduction, analyzing the development and present situation of the value distribution theory. The second part mainly introduces the basic knowledge of value distribution theory Nevanlinna first, second basic theorem, characteristic function, logarithmic derivative basic Lemma, etc.) and the basic knowledge of normality theory (convergent by spherical derivative, uniformly convergent, etc.) The concept of normal is Marty's normal rule, Zalcman's Lemma and Hurwitz's theorem. In the third part, the condition is weakened from .f 鈮，

本文编号：1838260