复合亚纯函数的亏量与增长性

亚纯函数F(z)称为复合，如果F(z)能分解为F(z)=f(f(z))， （1） 其中f是亚纯，g是整函数且f，g均非线性函数（当f是有理函数时，g可以是亚纯函数）。采用Nevanlinna理论的标准记号和结果，并引进记号△(a(z)，f)=1-limijf r→∞N(r，a(z)，f)/T（r，f）， （2）     

关于零级亚纯函数的Nevanlinna方向与Borel方向

本文研究了零级亚纯函数Borel方向与Nevanlinna方向的关系.应用Ahlfors覆盖曲面的几何方法,获得了部分零级亚纯函数关于型函数的.Borel方向一定是Nevanlinna方向,而这一结果至今未见有文献研究.     

亚纯函数及其微分多项式的唯一性

本文研究亚纯函数及其微分多项式的唯一性问题，证明了三个主要定理，改进并推广了K．Shibazaki，Yang C．C．，李江涛和顾永兴，仪洪勋等人的有关结果。     

MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

Applying Nevanlinna theory of the value distribution of meromorphic functions,we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form∑nj=1aj(z)f1(λj1)(z+cj) = R2(z, f2(z)),∑nj=1βj(z)f2(λj2)(z+cj)=R1(Z,F1(z)).(*)where λij(j = 1, 2, ···, n; i = 1, 2) are finite non-negative integers, and cj(j = 1, 2, ···, n)are distinct, nonzero complex numbers, αj(z), βj(z)(j = 1, 2, ···, n) are small functions relative to fi(z)(i = 1, 2) respectively, Ri(z, f(z))(i = 1, 2) are rational in fi(z)(i = 1, 2)with coefficients which are small functions of fi(z)(i = 1, 2) respectively.     

关于亚纯函数差分多项式的进一步结果

设f为一有穷级为ρ(f)的超越亚纯函数,μ和c作为一非零的常数.设n,m作为一正整数,且设s(z)作为一f的非零小函数.如果n≥m+4或者(m≥n+4),则差分多项式f~n(z)+μf~m(z+c)-s(z)在复平面上有无穷多个零点.     

分担多项式的亚纯函数的进一步结果(英文)

In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result：Let f（z）and g（z）be two transcendental meromorphic functions,p（z）a polynomial of degree k,n≥max{11,k＋1}a positive integer.If fn（z）f（z）and gn（z）g（z）share p（z）CM,then either f（z）=c1ec p（z）dz, g（z）=c2e ？c p（z）dz ,where c1,c2 and c are three constants satisfying（c1c2） n＋1 c2=-1 or f（z）≡tg（z）for a constant t such that tn＋1=1.     

亚纯函数多项式结合其导数的零点

研究p~t[f] aP~2[f](a≠0为常数）的零点问题．     

涉及微分多项式的亚纯函数分担值问题

This paper is devoted to studying the relationship between meromorphic functions f（z） and g（z） when their differential polynomials satisfy sharing condition weaker than sharing one value IM.     

单位圆内拟亚纯映射的Nevanlinna点

该文定义了单位圆内拟亚纯映射的Nevanlinna点与Borel点，并证明了单位圆内满足条件~lim_{r→1}{T(r)/{log1/(1-r)}}=∞的拟亚纯映射的Nevanlinna点与Borel点的存在性。     

单位圆内亚纯函数的Nevanlinna不等式和相关的奇异半径

应用Ahlfors覆盖曲面的方法,得到几个单位圆内亚纯函数的Nevanlinna基本不等式,应用它们证明了亚纯函数在单位圆内关于小函数的奇异半径的存在性,推广了复平面上亚纯函数奇异方向的相关结论.     

Zeros of Difference Polynomials of Meromorphic Functions

This research is a continuation of a recent paper, due to Liu and Laine, dealing with difference polynomials of entire function. In this paper, we investigate the value distribution of difference polynomials of meromorphic functions and prove some difference analogues to some classical results for differential polynomials.     

Growth of Entire Functions with Given Zeros and Representation of Meromorphic Functions

Mathematical Notes - Let $\Lambda = \{ \lambda n\}$ be a sequence of points on the complex plane, and let $\Lambda (r)$ be the number of points of the sequence $\Lambda$ in the disk $\{...     

线性微分多项式的零点与极点

对Frank-Weissenborn不等式中导数f~((k))能否被替换成一般的线性微分多项式a_0f+a_1f′+…+a_kf~((k))进行了研究,并彻底解决了这一问题.作为此结果的应用,Hayman-Yang不等式等几个已有的定理也得到了推广.例子表明,本文所得到的几个不等式的条件是基本的.     

关于亚纯函数微分多项式的值分布

Let f(z) be a meromorphic function andΨbe the differential polynomial of f which satisfies the condition of N(r, f) N (r, 1/f) = S(r, f). We obtain several results about the zero point of theΨand those results extend and improve the results of Yang and Yi in this paper.     

亚纯函数与其微分多项式的分担函数与正规族

设${\cal F}$为开平面内的区域$D$上的亚纯函数族, ${\cal F}$中任何函数$f(z)\in{\cal F}$, $f$的零点竽数至少为$k+1$.对于$D$内不等于零的解析函数$a(z)$.若$f(z)$与其微分多项式$D(f)$ IM分担$a(z)$,本文不仅得到${\cal F}$在$D$上正规, 而且得到相应于正规函数的结果.     

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.