Differential polynomials sharing a set of roots of unity with finite weight

Abstract

In this paper, we study the uniqueness problem of meromorphic functions when two differential polynomials share a set of roots of unity with finite weight. Our results not only generalize a result of Lahiri and Sinha [Commun. Korean Math. Soc., 35 (2020), 773-787], at the same time improve the recent results of Khoai and An [Advanced Studies: Euro-Tbilisi Math. J., 15 (2022), 39-51].