Uniqueness of certain differential polynomial of $L$-functions and meromorphic functions sharing a polynomial

Abstract

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an $L$-function when certain differential polynomial generated by them sharing a one degree polynomial. The main theorem of the paper extends and improves all the results due to W.J. Hao, J.F. Chen [Discrete Dyn. Nat. Soc. 2018, 2018, article ID 4673165], F. Liu, X.M. Li, H.X. Yi [Proc. Japan Acad. Ser. A Math. Sci. 2017, 93 (5), 41-46], P. Sahoo, S. Halder [Tbilisi Math. J. 2018, 11 (4), 67-78].