On the Uniqueness of L-Functions and Meromorphic Functions Under the Aegis of two Shared Sets

The paper presents general criteria for the uniqueness of a non-constant meromorphic function having finitely many poles and a non-constant L-function in the Selberg class when they share two sets. Our results provide the best cardinalities ever obtained in the literature improving all the existing results Li et al. (Lith. Math. J. 58(2), 249–262 (2018)), Kundu and Banerjee (Rend. Circ. Mat. Palermo (2) 70(3), 1227–1244 (2021), Banerjee and Kundu (Lith. Math. J. 61(2), 161–179 (2021) with regard to the most general setting. Further, we have exhibited a number of examples throughout the paper showing the far reaching applications of our results.