亚纯函数结合其导数的值分布

On The Value Distribution of Meromorphic Function

研究了亚纯函数结合其导数的值分布问题,得到了一个有趣的不等式,此不等式概括了方-杨和I.Lahiri和S.Dewan的结果,应用此不等式还得到关于θ(a(z);φ)的一个估计,这里φ(z)=α(z)f^nM[f],M[f]=(f′)^(n_1)(f″)^(n_2)…(f^((k)))^(n_k),n_1,n_2,…,n_k,n为非负整数满足:n_1+n_2+…+n_k≥1,α(z),a(z)(≠00,∞)为f的小函数.

In this paper,from investigating the value distribution of meromorphic function and its derivative,an inequality is obtained and generalizes the results of Fang and Yang, Lahiri I and Dewan S（[6]）.Further by this inequality,we get an estimate of φ（z）=α（z）fnM[f],M[f]=（f′）^n1（f″）^n2…（f（（k）^nk,n1,n2,…,nk,n,are all nonnegative integers and satisfy n1＋n2＋…＋nk≥1 andα（z）,a（z）（≠ 0,∞） be two small functions of f.