in this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. we obtain one results, which can give a negative answer to an uniqueness question relate to the bruck conjecture dealt by liu and yang. meanwhile, we also establish a difference analogue of the bruck conjecture for entire functions of order less than 2, ...

Let K/k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.