Acta mathematica scientia, Series B >
ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE
Received date: 2012-09-04
Revised date: 2013-04-22
Online published: 2014-05-20
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.
Key words： Complex difference; Borel exceptional value; sharing value
CHEN Zong-Xuan . ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 653 -659 . DOI: 10.1016/S0252-9602(14)60037-0
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