ON THE DIFFERENCE COUNTERPART OF BRCK'S CONJECTURE

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 △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.