亚纯函数微分多项式f^kQ[f]+P[f]的零点分布  

The Distribution of Zeros for Differential Polynomials f^kQ[f]+P[f]of Meromorphic 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：《数学年刊（A辑）》2013年第3期365-372,共8页Chinese Annals of Mathematics

基　　金：湖南省教育厅科研基金(No.09C228)的资助

摘　　要：研究了超越亚纯函数f的微分多项式f^kQ[f]+P[f]的零点分布.给出了以下结果:对于满足δ(∞,f)≥1-α>0(α为常数,0≤α<1)的超越亚纯函数f(x),若T(r,f)=O(log r)~2),则微分多项式f^kQ[f]+P[f](Q[f]≠0,P[f]≠0)在可数个圆盘并集之外有无穷多个零点,其中k>1+Γ_P+γP+α(1+Γ_Q+Γ_P-γP)/1-α,Γ_Q是Q[f]的权,ΓP和γP是P[f]的权和次数.This paper discusses the distribution of zeros for differential polynomial f^kQ[f]＋P[f] of trancendental meromorphic function f, and gives following result： Letting f be a trancendental meromorphic function with δ（∞,f）≥1-α〉0（α is a constant, 0≤α〈1）,such that T（r, f） = O（（logr）^2）, then the differential polynomial f^kQ[f]＋P[f]（Q[f]≠0,P[f]≠0） has infinitely many zeros outside the union of infinitely many discs, where k〉1＋ГP＋γP＋α（1＋ГQ＋ГP-γP）/1-α,ГQ is the weight of Q[f], ГP and γP are the weight and the degree of P[f], respectively.

关 键 词：整函数 亚纯函数 例外集 微分多项式 ε集 

分 类 号：O174.52[理学—数学]