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Using the value distribution theory, the author studied the uniqueness of meromorphic function concerning multiple value .

应用值分布理论,在涉及重值情况下进一步研究了亚纯函数唯一性理论中Gross 。F提出的一个问题,获得如下结果:设集合S ={ω∈C|P =aω7- 42ω2 +70bω- 30b2 =0 },其中a ,b为不等于零的常数,ab5≠ 2。

Based on different linear operators, some of the properties and characteristics of p-valent analytic functions and meromorphic multivalent functions were investigated extensively in this paper.

近年来,基于不同的线性算子,某些p叶解析函数类或亚纯函数类的性质和特征被广泛地研究。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为:亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式;椭圆函数,包括单周期函数、双周期函数;代数函数和代数体函数、Riemann曲面简介;Nevanlinna理论简介,包括特征函数、第一和第二基本定理、增长级等;复微分方程和复函数方程,等等。在教学内容上充分体现基础性、新颖性。

This thesis studies the uniqueness theory of meromorphic functions.

中文摘要:本论文主要研究的是亚纯函数的唯一性理论。

In 1925, R. Nevanlinna established two fundamental theorems of meromorphic functions and the study of the value distribution theory of modern times started.

Nevanlinna建立了亚纯函数的两个基本定理,开始了值分布理论的近代研究。

In this paper, we investigate the problem of the existence of transcendental meromorphic solutions of a type of algebraic differential equation and obtain a result.

文摘:讨论了一类代数微分方程的超越亚纯解的存在性问题,得到了一个结果。

The author discussed that growth of composite of entire functions and meromorphic functions with deficient functions.

讨论了具有亏函数的整函数与亚纯函数的复合函数增长性。

The main work of this thesis is that we investigatethe singular directions of the meromorphic solutions of the Schro¨der equations.

本文的主要工作是研究Schro¨der方程亚纯解的奇异方向。

The uniqueness theory of meromorphic functions mainly studies conditions underwhich there is only one function.

中文摘要所谓亚纯函数的唯一性理论主要讨论在什么情况下只存在一个函数满足给定的条件。

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.

中文摘要: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。

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