代数体函数

What s more, we wonder whether there are some qualities about algebroid function corresponding to meromorphic func-tion,specially, concerning deficiency, characteristic function,differential polynomial and so on.

而且一些亚纯函数中存在的性质在代数体函数中是否相应存在仍有待研究，特别是涉及亏量、特征函数及微分多项式等方面。

It s still imperfect about algebroid function, such as the relationship between the growth of algebroid function and the growth of irreducible equation coefficient, which defined the algebroid function.

中文摘要：关于代数体函数，有些结论仍不够完善，例如代数体函数的增长级与决定它的不可约方程的系数的关系。

The ν-value algebroid function w in the unit disk and its Borel points were discussed.

研究单位圆内ν值代数体函数w及其Borel点。

We prove the existence theorem of rationed with Borel points for meromorphic functions in the unit circle, discuss the operations of algebroid functions and the existence theorem of Nevanlinna direction of algebroid function dealing with mutiple values, and obtain some uniqueness theorems dealing with mutiple values of algebroid functions.

证明了单位圆内限定Borel点的亚纯函数的存在性定理，讨论了代数体函数的运算性质以及涉及重值的Nevanlinna方向的存在性定理，得到了一些涉及重值的代数体函数的唯一性定理； 2。

If w is a ν-value algebroid function of finite positive order in the unit disk, then there is a point eiθ0, such that w has at most 8ν-6 Borel exceptional values in angular domain Δ(θ0,δ).

对于单位圆内有穷正级ν值代数体函数w，必存在点eiθ0，使w在角域Δ(θ0，δ)内的Borel例外值之个数至多为8ν-6。

Differential equation; uniqueness theory; meromorphic function; algebroid function; unit disc

基础科学，数学，数学分析微分方程；唯—性理论；亚纯函数；代数体函数；单位圆

In this paper,the existence of commmon Borel point of algebroidal function and its derivatives in the unit disc is proved.

证明了单位圆内代数体函数及其导函数至少存在一个公共Borel点，结果和Valiron在1928年提出的关于亚纯函数及其导数是否存在公共Borel方向这一问题是相关的。

algebroidal function ; uniqueness theorem ; characteristic function

最后，我们应用新定义的加法，将杨乐的联系重值的唯一性定理推广到多值的代数体函数。设A，，…，A。是定义在复平面C上的一组没有

As an appliance, by applying the addition defined in this paper, the uniqueness theorem of meromorphic functions obtained by Yang Lo is generalized which consider its multiple values to multiple valued algebroidal functions.

本文明确地定义了加、乘运算，并证明了运算后的结果仍是代数体函数。为进一步的研究完善了理论基础。关于亚纯函数的唯一性定理有许多非常好的成果仁'1。杨乐创造了一种方法，结合重值更深人的研究了亚纯函数的值分布〔，一'了。

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。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。