ON THE DIFFERENCE COUNTERPART OF BRCK'S CONJECTURE  

作　　者：陈宗煊 

机构地区：[1]School of Mathematical Sciences,South China Normal University

出　　处：《Acta Mathematica Scientia》2014年第3期653-659,共7页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11171119)

摘　　要：In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then△f（z）-a/f（z）-a=a/a-α.In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then△f（z）-a/f（z）-a=a/a-α.

关 键 词：Complex difference Borel exceptional value sharing value 

分 类 号：O174.52[理学—数学] O241.3[理学—基础数学]