【作者】 戚建明；

【导师】 袁文俊；

【作者基本信息】 广州大学 ， 应用数学， 2007， 硕士

【摘要】 本文运用值分布理论和方法整理了亚纯函数各种例外值的概念,并且总结了例外值集之间的相互关系.本文的主要工作是研究Schro¨der方程亚纯解的奇异方向.第一章介绍了本文的研究工作,研究目的,学术背景等.第二章概述了值分布理论的基本知识及后几章中要用到的一些概念和记法,整理了亚纯函数a值点收敛指数的相关结论.第三章在亚纯函数原有的Picard例外值、Borel例外值、Nevanlinna例外值和Valiron例外值的基础上提出两个新的例外值,并且比较系统的总结了这些例外值集之间的相互关系.第四章整理了亚纯函数的各种奇异方向的定义,同时总结了它们之间的相互关系.第五章证明了Schro¨der方程f(sz) = R(f(z))在arg[s]/(2π)∈Q的条件下,它的任一亚纯解的任何一个方向都是T方向(精确T方向),同时也是Nevanlinna方向(其中|s| > 1且R(w)是一有理函数且deg[R]≥2).在最后一章给出一些待解决的问题.更多还原

【Abstract】 In this thesis, by using the theory and method of value distribution, we mainlyinvestigate the definitions and relationships among the except values and except valuessets of the meromorphic functions. The main work of this thesis is that we investigatethe singular directions of the meromorphic solutions of the Schro¨der equations. Thefirst chapter introduces the thesis’studying work, studying purpose, background andso on. The second chapter outlines the basic knowledge of value distribution theoryand some concepts and signs which are used in later chapters, also collects resultsabout convergence index of meromorphic at value a. The third chapter shows twonew except values based on the Picard except value、Borel except value、Nevanlinnaexcept value and Valiron except value, moreover concludes the relationships amongthe above except value sets. The forth chapter collects all kinds of singular direc-tions’definitions of meromorphic functions and concludes the relationships amongthe above directions. In the fifth chapter, the meromorphic solutions of the Schro¨derequations f(sz) = R(f(z)) are studied. If arg[s]/(2π)∈Q, then any meromorphicsolution has any direction as T direction (precise T direction)and Nevanlinna direc-tion as well(where |s| > 1 and R(w) is a rational function with deg[R]≥2). In thelast chapter, we give some open questions.更多还原