Abstract
In this paper, we investigate uniqueness problems of certain types of -difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where -differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function and a non-zero complex constant , for imply , where . This gives a partial answer to a question of Gross concerning a zero order meromorphic function and .
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