Askey-Wilson差分算子的全纯曲线值分布理论  

Value distribution theory of holomorphic curves for Askey-Wilson difference operators

作　　者：乔建永 代绘鑫 曹廷彬 Jianyong Qiao;Huixin Dai;Tingbin Cao

机构地区：[1]北京邮电大学理学院,北京100876 [2]南昌大学数学与计算机学院,南昌330031

出　　处：《中国科学：数学》2023年第7期953-972,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12071047和11871260)资助项目。

摘　　要：本文研究Askey-Wilson(AW)差分算子的全纯曲线值分布理论.首先,建立AW差分算子全纯曲线到复射影空间的第二基本定理,这个定理推广了Chiang和Feng(2018)得到的复平面上亚纯函数第二基本定理的结果.其次,应用第二基本定理并引入AW-不变量的概念,得到AW差分算子的Picard型定理.最后,给出AW差分多项式的Tumura-Clunie型定理.In this paper,we investigate the value distribution theory of holomorphic curves for Askey-Wilson(AW)difference operators.Firstly,we establish the second main theorem of holomorphic curves for AW difference operators into complex projective spaces,which generalizes Chiang and Feng(2018)'s second main theorem for meromorphic functions.Secondly,by our second main theorem,we obtain a Picard type theorem for AW difference operators with the concept of AW-invariant.Finally,we give the Tumura-Clunie theorem for AW difference polynomials.

关 键 词：Askey-Wilson差分算子 全纯曲线 第二基本定理 Picard定理 Tumura-Clunie定理 

分 类 号：O174.52[理学—数学]