本文選題：亞純函數(shù) + 微分多項式�。� 參考：《南京師范大學(xué)》2015年碩士論文

【摘要】：正規(guī)族理論是復(fù)分析中的重要課題,函數(shù)值分布是研究正規(guī)定則的有力工具.本文主要研究了亞純函數(shù)正規(guī)族和值分布方面,得到了一些好的結(jié)論.論文安排如下：前言里,我們簡單敘述了值分布論與亞純函數(shù)正規(guī)族的發(fā)展脈絡(luò)及此領(lǐng)域的某些研究成果.第一章,我們給了這篇文章中所需的基礎(chǔ)理論：值分布論與正規(guī)族的基本概念,記號及基本結(jié)果.第二章,我們運用正規(guī)族理論研究了一類關(guān)于微分多項式的亞純函數(shù)的值分布,使得結(jié)果一定程度上改進了徐焱和仇惠玲在[16]中的結(jié)果.第三章,我們研究并得到了一個關(guān)于分擔(dān)函數(shù)的正規(guī)定則.推廣戚建明和朱泰英[11],鄒海斌[22]等人的相關(guān)結(jié)果.第四章,我們研究并得到了一類關(guān)于微分多項式的正規(guī)定則,推廣和改進了蘭富祥[6]等人的相關(guān)結(jié)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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O174.52

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本文編號：1911607