ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE

doi:10.1016/S0252-9602(14)60037-0

摘要/Abstract

摘要：

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

关键词: Complex difference, Borel exceptional value, sharing value

Abstract:

Key words: Complex difference, Borel exceptional value, sharing value

中图分类号:

39A10

陈宗煊. ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE[J]. 数学物理学报(英文版), 2014, 34(3): 653-659.

CHEN Zong-Xuan. ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE[J]. Acta mathematica scientia,Series B, 2014, 34(3): 653-659.

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