整函数与其差分算子的唯一性定理

本文证明了:如果有限级非常数整函数f和它的差分算子△_η~nfCM分担小函数α,且0为f的亏值,那么(△__η~nf-α)/(f-α)≡c,其中c为非零常数.同时,还研究了整函数f和它的差分算子△_ηf,△_η~fCM分担小函数α的唯一性问题.     

整函数及其差分分担有限集的唯一性

研究了整函数及其差分多项式分担有限复数集的唯一性,得到了如下结果:设S_m={1,ω,…,ω~(m-1)},其中ω=cos(2π/m)+i sin(2π/m),c为非零有限复数,n(>5),m(≥2)均为正整数.如果f(z),g(z)为有限级整函数,满足E(S_m,f(z)~n(f(z)-1)f(z+c))=E(S_m,g(z)~n(g(z)-1))g(z+c)),那么f(z)≡g(z).     

涉及差分算子分担的亚纯函数的唯一性

研究并证明了两个涉及亚纯函数及其差分算子分担的唯一性定理,该结论改进了已有的相关研究结果.     

涉及整函数差分算子的唯一性定理

作者研究了关于有穷级整函数两个差分算子的分担值问题,证明了:令f(z)是满足λ(f-a(z))＜p(f)的有穷级超越整函数,其中a(z)(∈ S(f))是整函数且满足p(a(z))＜1,并令η(∈C)是常数且满足Δ2ηf(z)≠0.如果Δ2ηf(z)和Δηf(z)CM分担Δηa(z),其中Δηa(z)∈S(Δ2ηf(z...     

整函数及其差分的唯一性

设f是一个有穷级的超越整函数,a,b,c是3个有穷复数,满足c≠0,a≠b,且n为正整数.如果a是f的Borel例外值,且Δ_c~nf(z)与f(z)IM分担b,则f(z)=a+Ae~(Bz),其中A,B为两个非零常数.     

涉及差分算子的亚纯函数的唯一性

本文研究涉及差分算子的亚纯函数的唯一性问题,得到一个唯一性定理:设f是一个级不小于2的有限级整函数,η是非零复数,a(z)是不恒等于0的整函数,满足ρ(a)ρ(f)和λ(f-a)ρ(f).若f-a与Δnηf-a(n=1或2)CM分担0,则f(z)是整数级的,且ρ(a)=1或ρ(a)≥ρ(f)-1,f(z)=a(z)+[Δnηa(z)-a(z)]eA(z),其中A(z)是一个次数和ρ(f)相等的多项式.     

整函数与其导数具有一个分担值

改进了H.Zhong的一个结果.     

涉及分担集的整函数的唯一性

In this paper,uniqueness of entire function related to shared set is studied.Let f be a non-constant entire function and k be a positive integer,d be a finite complex number.There exists a set S with 3 elements such that if f and its derivative f（k）satisfy E（S,f）= E（S,f（k））,and the zeros of f（z）-d are of multiplicity ≥ k ＋ 1,then f = f（k）.     

整代数体函数与其导函数的增长级

对整代数体函数与其导函数的增长性进行了研究,得到了整代数体函数与其导函数的特征函数之间关系式,并证明了它们具有相同的级和下级,从而将亚纯函数的相应结果推广到了整代数体函数.     

与其导数分担一个值的整函数(英文)

主要得到与其导数分担一个值的整函数的一个唯一性定理，推广并改进了Gundersen与杨连中的有关结果．     

分担1 IM公共值的整函数的唯一性定理(英文)

主要研究具1 IM分担值的整函数的唯一性问题,获得的定理推广了林伟川,方明亮,华歆厚,C.C.Yang等人的系列结果.     

The Uniqueness of Entire Functions with Their Derivatives

§ 1.Introduction　 By a“meromorphic function” we mean a function that is meromorphic in the wholecomplex plane.It is assumed that the reader is familiar with notations of Nevanlinnatheory such as T(r,f) ,m(r,f) ,N (r,1f) ,S(r,f ) and so on that can be found,forinstance,in[1 ] or[2 ] .Let f and g be two meromorphic functions and a be a complexnumber. We say that f and g share the value a CM (counting multiplicity) if f -a andg-a have the same zeros with the same multiplicity,and denote th…     

与高阶导数有公共不动点的整函数

本文证明了如果f是非常数整函数满足超级σ_2(f)<1/2,k是一正整数,如果f和f(k)有公共不动点z CM,那么f~((k))(z)-z=c(f(z)-z),其中c是非零常数.     

Entire Functions Sharing an Entire Function of Smaller Order with Their Diference Operators

We study a uniqueness question of entire functions sharing an entire function of smaller order with their diference operators,and deal with a question posed by Liu and Yang.The results in this paper extend the corresponding results obtained by Liu–Yang and by Liu–Laine respectively.Examples are provided to show that the results in this paper,in a sense,are the best possible.     

Normal Families and Uniqueness of Entire Functions and Their Derivatives

Let f be a nonconstant entire function; let k ≥ 2 be a positive integer; and let a be a nonzero complex number. If f（z） = a→f′（z） = a, and f′（z） = a →f^（k）（z） = a, then either f = Ce^λz ＋ a or f = Ce^λz ＋ a（λ - 1）/）λ, where C and ）, are nonzero constants with λ^k-1 = 1. The proof is based on the Wiman-Vlairon theory and the theory of normal families in an essential way.     

On the Uniqueness Theory of Entire Functions and Their Difference Operators

In this paper, we consider uniqueness problems on entire functions that share a small periodic entire functions with their shifts and difference operators, we improve also some results due to B. Chen, Z. X. Chen and S. Li.