亚纯函数的Jackson差分算子和Askey-Wilson差分算子的对数Borel例外值  

Logarithmic Borel Exceptional Values for Jackson Difference Operators and Askey-Wilson Difference Operators of Meromorphic Functions

作　　者：王钦 马飞 王玲 张石梅 WANG Qin;MA Fei;WANG Ling;ZHANG Shimei(School of Mathematical Sciences,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《复旦学报（自然科学版）》2024年第6期685-694,710,共11页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(11861023);2020年贵州师范大学博士科研启动项目(0520103)。

摘　　要：利用亚纯函数的值分布理论,研究了亚纯函数的Jackson差分算子和Askey-Wilson差分算子的对数Borel例外值的存在性问题,分别刻画了有穷对数级的非常数亚纯函数f与Jackson差分算子D n qf或Askey-Wilson差分算子D AW f的对数Borel例外值之间的关系。The existence problem of logarithmic Borel exceptional values for Jackson difference operators and Askey-Wilson difference operators of meromorphic functions is studied by using Nevanlinna theory of meromorphic functions,and the relationships concerning logarithmic Borel exceptional values between nonconstant meromorphic functions f with finite logarithmic order and the of Jackson difference operator D n qf or Askey-Wilson difference operator D AW f are investigated.We proved:let f be a nonconstant meromorphic function with finite logarithmic order,q∈C satisfying 0<|q|<1,n∈N,such that D n qf 0.Then for a∈C and b∈C\{0},lim sup r→∞log+{n(r,a,f)+n(r,b,D n qf)}log log r=ρlog-1.With regard to Askey-Wilson difference operator D AW f,we also obtain the same results.

关 键 词：亚纯函数 对数级 对数Borel例外值 Jackson差分算子 Askey-Wilson差分算子 

分 类 号：O174.52[理学—数学]