摘要
本文考虑了关于亚纯函数结合其导数涉及重值的辐角分布方面的问题,主要证明了:定理1 设 f(x)是λ级亚纯函数,0<λ<∝,则存在一条由原点出发的半直线 B:arg z=θ_0,(0≤θ_0<2π)使得对于任意正数ε,一切有穷复数 a 与一切有穷非零复数 b 有:(?)(log{n(r,θ_0,ε,f)+n_(k-1)(r,θ_0,ε,f=a)+n_(l-1)(r,θ_0,ε,f^(m)=b)})/log r其中 k,l,m 为正数且满足条件 (m+1)/k+1/l<1.本文还对定理1作了推广。
This paper concerns with the angle distribution of meromorphic function.The main results are as following:Theorem 1:let f(z) be a meromorphic function of order λ(0<λ<∞),then there exists a direction B:argz=θ_0(0≤θ_0≤2π),such that forany ε>0,any finite complex number a and any finite non-zero complex number b:(?)(log{n(r,θ_0ε,f)+n_(?)(r,θ_0,ε,f =a)+n_(?)(r,θ_0,ε,f^(m)=b)})/(log r)=1where k,l,m are the positive integers satisfying (m+1)/k+1/l<1.Also,this paper improves Theorem 1.
出处
《数学杂志》
CSCD
北大核心
1990年第1期21-32,共12页
Journal of Mathematics
