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] in Meromorphic Function f(z)

作　　者：谭卫平[1] 詹小平[1] 

机构地区：[1]湖南第一师范学院数理系,湖南长沙410002

出　　处：《数学的实践与认识》2009年第2期149-157,共9页Mathematics in Practice and Theory

基　　金：湖南省教育厅科研基金资助项目(01C045)

摘　　要：从例外集的角度研究了亚纯函数微分多项式fkQ[f]+P[f]的零点分布,证明了:对于满足δ(∞,f)1-α>0的超越亚纯函数f(z),微分多项式fkQ[f]+P[f]在不含极点的可数个圆盘并集之外有无穷多个零点,其中k>1+ΓP+γP+α1(-1+αΓQ+ΓP-γP),ΓQ是Q[f]的权,ΓP,γP是P[f]的权和次数.本文推广了Hayman,Anderson,Langley等人的结论.The distribution of zeros for differential polynomials f^kQ [f] ＋ P[f] in meromorphic function f（z） was studied from a viewpoint of exceptional set. we prove the following result which improved the result of Hayman, Anderson and Langley. Suppose that f is a transcendental meromorphic function such that δ（∞,f）≥1-α〉0. Then f^kQ[f]＋P[f] has infinitely many zeros outside the union of the discs which do not contain the poles of f and Q[f], where k〉1＋ΓP＋γP＋α（1＋ΓQ＋ΓP-γP）/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：O174.52[理学—数学] O156.4[理学—基础数学]