一类缓慢增长的亚纯函数微分多项式的例外集  

The Exceptional Set for the Differential Polynomials of a Class of Slowly Growing Meromorghic Function

作　　者：谭卫平[1] 詹小平[1] 

机构地区：[1]湖南第一师范学院数学系,长沙410205

出　　处：《数学物理学报（A辑）》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

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).

关 键 词：整函数 亚纯函数 例外集 微分多项式 ε集 

分 类 号：O117[理学—数学]