亚纯函数位移与差分的唯一性

发布时间：2018-03-14 04:45

本文选题：亚纯函数　切入点：位移　出处：《南京师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：亚纯函数的唯一性是值分布论的重要且活跃的研究课题之一.近些年来,唯一性的研究已经推广到差分领域.本文主要研究亚纯函数关于位移、q-位移及差分分担常数(或小函数)的问题.论文安排如下：前言里,我们简单叙述了值分布论和唯一性理论发展的脉络及此领域的某些研究成果.第一章,我们给出了本文所需要的基础知识：亚纯函数的值分布,唯一性理论的一些基本概念、记号及基本结果.第二章,我们研究了亚纯函数关于位移、差分分担小函数的唯一性问题,得到了仪洪勋和杨重骏[19]等关于导数唯一性的相应位移与差分的结果,推广了刘永和祁晓光[20]等人关于差分唯一性的相关结果.第三章,我们主要研究了亚纯函数q-位移的唯一性,结果推广了祁晓光和杨连中[22],Zhang和Korhonen[24],王琼燕和叶亚盛[25]等人的相关结果.
[Abstract]:The uniqueness of meromorphic functions is one of the important and active research topics in the theory of value distribution. The study of uniqueness has been extended to the field of difference. In this paper, we mainly study the problem of displacement q-displacement and differential sharing constant (or small function) of meromorphic functions. We briefly describe the development of the theory of value distribution and uniqueness and some research achievements in this field. In chapter 1, we give the basic knowledge needed in this paper: the value distribution of meromorphic functions and the basic concepts of uniqueness theory. In the second chapter, we study the uniqueness of meromorphic functions with respect to displacement and differential sharing small functions, and obtain the corresponding displacement and difference results on the uniqueness of derivatives, such as Yi Hongxun and Yang Zhong-jun [19]. In chapter 3, we mainly study the uniqueness of q-displacement of meromorphic functions. Results the results of Qi Xiaoguang and Yang Lianzhong [22] Zhang and Korhonen [24], Wang Qiongyan and Ye Yasheng [25] were generalized.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O174.52

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