Uniqueness of $\boldmath{L}$-Function and certain class of meromorphic function under two weighted shared sets of least cardinalities

Abstract

In this article we study the uniqueness problem of an $L$ function belonging to the Selberg class with an arbitrary meromorphic function having finite poles sharing two sets. Actually to answer a question raised by Lin-Lin [ Filomat, $\mathbf{30}$(2016), 3795-3806], we have significantly improved a recent result [Rend. Del. Math. Palermo, (2020)(published online)] of the authors and that of Chen-Qiu [Acta. Math. Sci., $\mathbf {40B}(4)$ (2020), 930-980]. Moreover we have also been able to provide the best possible answer of another unsolved question of [ Filomat, $\mathbf{30}$(2016), 3795-3806] and investigated the results of the same in the light of finite weighted sharing.