关于亚纯函数及其k阶导数的惟一性  

On the uniqueness of meromorphic functions and their k-th derivatives

作　　者：郑赛莺[1] 

机构地区：[1]宁德师范学院数学系,福建宁德352100

出　　处：《纺织高校基础科学学报》2010年第2期206-208,共3页Basic Sciences Journal of Textile Universities

摘　　要：研究亚纯函数与其k阶导数分担一个IM公共值和一个CM公共值在一定条件下的惟一性问题,考虑吴桂荣有关亚纯函数及其k阶导数具有1CM公共值在一定条件下的惟一性问题,利用构造辅助函数结合Nevanlinna第二基本定理的方法证明了:设f与g为非常数亚纯函数,1为f(k)与g(k)的CM公共值,k∈N,∞为f与g的IM公共值,如果(k+1)-Nr,1f+(k+1)-Nr,1g+2(k+1)N-(r,f)+(1/2)N-D(r,f)<(λ+o(1))T(r)(r∈I),其中λ<1/2,T(r)=max{T(r,f),T(r,g)},-ND表示相应于f与g所有极点的重级均不相同的f极点的精简密指量,则f(z)≡g(z)或者f(k)(z).g(k)(z)≡1.The uniqueness problem of two meromorphic functions with their k-th derivatives share one IM value and CM value under certain conditions is discussed.And it is considered that the uniqueness problem of two meromorphic functions with their k-th derivatives share 1 CM under certain conditions by Wu Guirong.By using the method of constructing auxiliary functions and the Nevanlinna second fundamental theorem,it is proved that let f and g be two non-constant meromorphic functions,if f^（k） and g^（k） share one CM,k be a positive integer,and f and g share ∞ IM,and （k＋1）N^-（r/1/f）＋（k＋1）N^-（r,1/g）＋2（k＋1）N^-（r,f）＋（1/2）N^-D（r,f）（λ＋o（1））T（r）（r∈I）,where λ1/2,T（r）=max{T（r,f）,T（r,g）},It is supposed that z is a pole of f order p,a pole of g orter q.By N^-D（r,f） denoted that counting function of those poles of f with multiplicities p and q with multiplicities q（p≠q）（each ploe is counted only once）,then f（z）≡g（z） or f^（k）（z）·g^（k）（z）≡1.

关 键 词：亚纯函数 惟一性定理 亏值 

分 类 号：O174.52[理学—数学]