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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]

Let 0 < γ1 < ⋯ ≤ γk ≤ ⋯ be the sequence of imaginary parts of nontrivial zeros of the Riemann zetafunction. In [R. Macaitienė and D. Šiaučiūnas, Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function, Lith. Math. J., 59(1):81–95, 2019] a joint universality theorem on the approximation of analytic functions by shifts of the Hurwitz zeta-functions ζ(s + ihγk, α1), ..., ζ(s + ihγk, αr) has been obtained. In the paper, we prove universality theorems for the compositions F(ζ(s + ihγk, α1), ..., ζ(s + ihγk, αr)) for some classes of operators in the r-dimensional space of analytic functions. [ABSTRACT FROM AUTHOR]