关于代数体函数的Nevanlinna第二基本定理  

ON THE NEVANLINNA SECOND FUNDAMENTAL THEOREM OF ALGEBROID FUNCTIONS

作　　者：涂振汉[1] 

机构地区：[1]华中理工大学

出　　处：《数学杂志》1995年第1期72-76,共5页Journal of Mathematics

摘　　要：设为复平面上的整函数且没有公共零点，令ｋ＋１ｉ是在复数域上的极大线性无关数。设ｗ＝ｗ（ｚ）由下列不可约方程Ａ＿ｎ（ｚ）ｗ￣ｎ＋Ａ＿（ｎ－１）（Ｚ）ｗ￣（ｎ－１）＋…＋Ａ＿１（ｚ）Ｗ＋Ａ＿０（ｚ）＝０所定义。我们称ｗ＝ｗ（ｚ）为ｎ值Ｋ型代数体函数（１≤ｋ≤ｎ）。Let k+1 be the maximal linear independent nuinber of on the complex number field,lf w(z)is defined by the irreducible equation A_nw￣n+A_(n-1)(z)w￣(n-1)+…+A_1(z)w+A_0(z)=0 where are entire functions on C and have no conmon zero, w(z)is called n一valued k type algebroid function(1≤k≤n)。In this paper、we have Theorem 1 Let w(z)be n一valued k type algebroid function and a_i (i=1,2,…,p)be p distinct complex numbers(finite or infinite),Then where in the multiplicity of every zero point of w(z)-a_i is counted up to k tires.Corollary 1 Let w(z)be n一valued k type algebroid function. Then we have the defect relaticnwhereAs an applicalion of Theorew1,We have unlqueness the theorem of algebroidfunctions. Theorem 2 Letw_1(z)、w_2(z) be n_1一valued k_1 type and n_2 val ued k_2typealgebroid funclion respectively. Set n=max{n_1,n_2}and k=min{k_1,k_2}.Let a_i∈CU{∞}(i=1,2,…,4n+2-k)be 4n+2-kdistinct complex numbers.If w_1(a_i)=w_2(a_i)(counted the multiplicity up to max{k_1,k_2}times)fori=1,2,…,4n+2一k,then w_1(z)≡w_2(z).

关 键 词：代数体函数 第二基本定理 NEVANLINNA 

分 类 号：O174.53[理学—数学]