亚纯函数的幅角分布及其增长性  

ANGULAR DISTRIBUTION OF MEROMORPHIC FUNCTIONS AND THEIR GROWTH

作　　者：王文昌[1,2] 顾永兴[1,2] 

机构地区：[1]第三军医大学预防医学系 [2]重庆大学

出　　处：《数学杂志》1997年第2期277-282,共6页Journal of Mathematics

基　　金：国家自然科学基金

摘　　要：本文考虑了亚纯函数的幅角分布及其增长性的关系，得到了如下定理：设ｆ（ｚ）为亚纯函数，下级μ（μ＜＋∞，ａｒｇｚ＝θｋ（ｋ＝１，２，…，ｑ；０≤θ１＜θ２＜…＜θｑ＜２π，θｑ＋１＝θ１＋２π）为ｑ（１≤ｑ＜＋∞）条半直线使对ε＞０有：ｌｉｍｒ→∞ｌｏｇ＋ｎ（∪ｑｋ＝１Ω（θｋ＋ε，θｋ＋１－ε；ｒ），ｆ＝ｘ）ｌｏｇｒ≤ρ＜＋∞ｘ＝０，∞则当存在一非负整数ｌ使ｆ（ｌ）（ｚ）（ｆ（０）（ｚ）＝ｆ（ｚ））有一亏函数ａ（ｚ）（ａ（ｚ）０）时，必有λ≤ｍａｘ（πω，ρ），其中λ为ｆ（ｚ）的级，ω＝ｍｉｎ１≤ｋ≤ｑ（θｋ＋１－θｋ）．In this paper, we consider the relation between angular distribution of meromorphic functions and their growth, and obtain the following result:Suppose that f(z) is a meromorphic function with lower order μ(μ<+∞) and that arg z= θ k(k=1,2,…,q,0≤θ 1<θ 2<…<θ q<2π,θ q+1 =θ 1+2π) is q(1≤q<+∞) rays such that for any ε>0  lim r→∞ log + n (∪qk=1Ω(θ k+ε,θ k+1 -ε;r),f=x) log r≤ρ<+∞ x=0,∞Then, if there exists a non negative integer l such that f (l) (z) (l=0 means f (0) (z)≡f(z)) has a deficient function a(z) (a(z)0), We have λ≤ max ( ρ,πω), where λ is a order of f(z) and ω= min 1≤k≤q(θ k+1 -θ k).

关 键 词：亚纯函数 幅角分布 增长性 

分 类 号：O174.52[理学—数学]