Uniqueness on Difference Operators of Meromorphic Functions of Infinite Order  

作　　者：Hui LI Ming Liang FANG Xiao YAO 

机构地区：[1]School of Science,China University of Mining and Technology,Beijing 100083,P.R.China [2]Institute of Mathematics,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100190,P.R.China [3]School of Sciences,Hangzhou Dianzi University,Hangzhou 310012,P.R.China [4]School of Mathematical sciences and LPMC,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第2期511-527,共17页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.12071047,12171127,11901311);National Key Technologies R&D Program of China(Grant No.2020YFA0713300)。

摘　　要：We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.

关 键 词：UNIQUENESS meromorphic functions difference operators infinite order 

分 类 号：O174.52[理学—数学] O177[理学—基础数学]