亚纯函数相关于Hayman猜想的正规定则推广(英文)

On normal criteria of meromorphic functions related a Hayman Conjecture

设F是区域D上的亚纯函数族,n N.Hayman猜想的正规定则是:如果族F中的每个f(z)都满足fn(z)f′(z)≠1,那么F在D上正规.文章的主要结果推广了它,允许fn(z)f′(z)-1取零值,但在这些零值点处的f(z)值有所限制.

Let F be a meromorphic function family on domain D, n ∈ N. The conjecture of Hayman says： If each functionf（z） of family F satisfiesf f^n（z）f′（z）≠1 ,then F is normal in D. In the paper we generalize it by allowing f^n（z）f′（z）-1 to have zeros, but restricting the valuesf（z） can take at the zeros of f^n（z）f′（z）-1.