摘要
从例外集的角度研究了亚纯函数微分多项式的值分布,证明了:对于满足δ(∞.f)≥1-α>0的超越亚纯函数f(z).若T(r,f)=O((logrr)~2).则微分多项式f^kQ[f]在可数个圆盘并集之外取任何非零有限复数无穷次,其中k>(1+α(1+ΓQ))/1-α,ΓQ是Q[f]的权.
The value distribution of differential polynomials f^kQ[f]in meromorphic function f(z) was studied from a viewpoint of exceptional set.We prove the following result.Suppose that f is a transcendental meromorphic function such that δ(∞,f)≥1-α>0.Then if T(r,f)=O((logr)~2),f^kQ[f]asumes any non-zero finite complex number infinitely often outside the union of the discs,where k>(1+α(1+Γ_Q))/(1-α).
出处
《数学物理学报（A辑）》
CSCD
北大核心
2013年第4期728-734,共7页
Acta Mathematica Scientia
基金
湖南省教育厅科研基金(09C228)资助
关键词
整函数
亚纯函数
例外集
微分多项式
ε集
Entire function
Meromorphic function
Exceptional set
Differential polynomial
ε set
