亚纯函数的差分多项式  

On Certain Type of Difference Polynomials of Meromorphic Functions

作　　者：张然然 黄志波[2] ZHANG Ranran;HUANG Zhibo(Department of Mathematics,Guangdong University of Education,Guangzhou510303,China;Corresponding author. School of Mathematical Sciences,South China Normal)

机构地区：[1]广东第二师范学院数学系,广州510303 [2]华南师范大学数学科学学院,广州510631

出　　处：《数学年刊（A辑）》2019年第2期127-138,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11801093;No.11871260);广东省自然科学基金(No.2016A030313745;No.2018A030313508)的资助

摘　　要：假设函数f(z)是亚纯函数,H(z,f)是关于f(z)的差分多项式,s(z)是关于f(z)的小函数,考察了差分多项式f(z)~nH(z,f)-s(z)的零点分布问题.首先得到了差分多项式f(z)~nH(z,f)-s(z)的零点计数函数和函数f(z)的特征函数以及极点计数函数之间的一些不等式估计,再根据这些不等式,建立了Hayman关于亚纯函数的一个经典结果的差分模拟.In this paper, the authors investigate zeros of difference polynomials of the form f(z)^nH(z, f)-s(z), where f(z) is a meromorphic function, H(z,f) is a difference polynomial of f(z) and s(z) is a small function. The authors first obtain some inequalities for the relationship of the zero counting function of f(z)^nH(z,f)-s(z) and the characteristic function and pole counting function of f(z). Based on the above inequalities, the authors then establish some difference analogues of a classical result of Hayman for meromorphic functions.

关 键 词：差分多项式 亚纯函数 值分布 

分 类 号：O174.52[理学—数学]