亚纯函数的正规族(英文)  

NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS

作　　者：徐焱[1] 

机构地区：[1]南京师范大学数学系,南京210024

出　　处：《数学杂志》2001年第4期381-386,共6页Journal of Mathematics

基　　金：Universities and Colleges Foundation of Department of Education ofJiangsu Province( 0 0 KJB1 1 0 0 0 4)

摘　　要：关于正规族的 Hayman猜测目前已完全证实 ,本文考虑把 Hayman猜测中的 f′换为一般的f( k) ,得到一个更为一般的结果 ,由此改进和推广了陈怀惠 ,顾永兴 ,华歆厚 ,庞学诚与 W.Recently, people have proved Haymans conjecture on normal family completely which asserts that a family of meromorphic functions is normal if every function f in the family satisfies f-af 3≠b, where a and b are fixed complex numbers with a≠0,∞ and b≠∞ . In this paper, by replacing f by f (k) and setting a condition for the order of poles and zeros of f , we obtain a general theorem: a family of meromorphic functions is normal if every function f in the family satisfies f (k) -af n≠b and has only poles and zeros of order at least l and t respectively, where positive integers n, k, l and t satisfies n-1-(k+1)/l-1/t>0. This theorem improves and generalizes previous results in this direction due to H. Chen,Y.Gu,X.Hua,,X. Pang and W. Schwick.

关 键 词：亚纯函数 极点 零点 正规族 Hayamn猜测 

分 类 号：O174.52[理学—数学]