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The purpose of the paper is to study the uniqueness problem of an L function in the Selberg class sharing one or two sets with an arbitrary meromorphic function having only finitely many poles. We manipulate the notion of weighted sharing of sets to improve a result of Q.Q. Yuan, X.M. Li, and H.X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249–262, 2018]. Most importantly, we have pointed out a number of logical shortcomings in the two results of P. Sahoo and S. Haldar [Results on L functions and certain uniqueness question of Gross, Lith. Math. J., 60(1):80–91, 2020]. As an attempt to rectify the results of Sahoo and Halder, we have improved them by presenting their accurate forms and proofs as far as practicable. [ABSTRACT FROM AUTHOR]

In this paper, we study the value distribution of L-functions in the Selberg class and concentrate on the uniqueness questions of L-functions that share one or two sets with an arbitrary meromorphic function. The results obtained in this paper improve the recent results due to Q.-Q. Yuan, X.-M. Li, and H.-X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249–262, 2018] and also extend a result due to B.Q. Li [A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071–2077, 2010]. [ABSTRACT FROM AUTHOR]