关于代数体函数Borel方向的一个结果

A Result of Borel′s Direction for Algebroid Functions

中文关键词:  代数体函数  覆盖曲面  Borel方向

英文关键词:algebroid function  covering surfaces  Borel′s direction.

中文摘要:

      本文证明了下列定理：设ｗ＝ｗ（ｚ）为｜ｚ｜＜∞上的υ值代数体函数，它的级满足０＜ρ＜∞，则存在一条方向Ｌ：ａｒｇｚ＝θ_０（０≤θ_０＜２π），使得对于任意给定的δ，０＜δ＜π/２，在角域Δ（θ_０，δ）内,对任何值ａ成立，至多除去３υ－１个例外 .

英文摘要:

      In this paper, the following theorem is obtained: Let w=w(z) be a υ valued algebroid function of finite order ρ>0 for |z|<∞ , then there exists a direction L: arg z=θ_０(0≤θ_０<2π) , such that for any δ>0(δ<π/2 ), with 3υ-1 possible exceptions for any value of a . Where n³⁾ (r,Δ(θ_０,δ),a) is the numbers of distinct zeros with multiplicity ≤3 of w(z)-a in Δ(θ_０,δ)∩{|z|≤r} .