一类亚纯函数多项式的值的分布

Distribution of values of a class of polynomials with meromorphic functions

设f(z)是复平面上的亚纯函数,P[f]是f的n次常系数多项式,Q[f]是f的微分多项式,满足-N(r,f)+-N r,P′1+Q=S(r,f),其中Q[f]的次数vQ≤n-2,本文考虑P′[f]+Q[f]的值分布,推广了Hayman K W,Clunie J,Wues E等人关于整函数的结果,进一步改进了张占亮和李伟等人的相关研究结果.

Let f（z） be a meromorphic function,P[f] a constant-coefficient polynomial in f raised to zpower, and Q[f] a differential polynomial in f, that all of them satisfy N^-（r,f）＋N^-（r,P＇＋Q/1）=S（r,f）, in which the power of Q[f] vQ≤n-2. In this paper,the value distribution of differential polynomials in the form of P＇[f]＋Q[f] was studied, the results given by Hayman W K, Clunie J and Mues E were extended, and those of Zhang Zhan-liang,Li Wei, et al were improved further.