發(fā)布時(shí)間：2018-05-03 11:11

  本文選題：亞純函數(shù) + 例外值��； 參考：《湖北大學(xué)》2015年碩士論文

【摘要】：1907年,P.Montel引進(jìn)引進(jìn)正規(guī)族的定義后,值分布理論得到了新的發(fā)展,其對(duì)值分布理論具有極其重要的意義；隨后20世紀(jì)20年代,R.Nevanlinna第一基本定理,第二基本定理的引入帶來了值分布理論的空前發(fā)展；而后Marty正規(guī)定則和Zalcman引理的發(fā)現(xiàn)后,為人們逆向?qū)ふ艺?guī)性帶來了理論依據(jù),為人們尋找正規(guī)性帶來了新的思路與視野。隨之以后,我國的一部分?jǐn)?shù)學(xué)家也為值分布理論的發(fā)展作出了重大貢獻(xiàn),特別是熊慶來,楊樂,顧永興,方明亮等人的研究處于國際前沿�；谡�(guī)性理論的探討,本文主要分成五部分：第一部分是引言,分析值分布理論的發(fā)展與現(xiàn)狀。第二部分主要介紹值分布理論的基礎(chǔ)知識(shí)(Nevanlinna第一、第二基本定理,特征函數(shù),對(duì)數(shù)導(dǎo)數(shù)基本引理等)和正規(guī)性理論的基本知識(shí)(按球面導(dǎo)數(shù)收斂、一致收斂,正規(guī)的概念,Marty正規(guī)定則,Zalcman引理以及Hurwitz定理)。第三部分由基本的Hayman司題出發(fā),將條件由.f≠0,f(n)≠1減弱為fnf’≠1,再換成fn-f’≠1,另外條件n≥4也逐步變?nèi)踔羘≥2,還有逐步將例外值向例外函數(shù),函數(shù)列進(jìn)行推進(jìn),逐步改善條件。第四部分同樣由Hayman問題出發(fā),不過與第二部分不同的是從分擔(dān)值方面進(jìn)行考慮,類似于第二部分逐步減弱條件,使得所得定理更加實(shí)用。第五部分結(jié)論與展望對(duì)當(dāng)代值分布理論的探討進(jìn)行說明,并對(duì)相應(yīng)的正規(guī)定則進(jìn)行假設(shè)與推測。
[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，

本文編號(hào)：1838260