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In 2007, H. Mishou proved the universality theorem on the joint approximation of a pair of analytic functions by the shifts of the Riemann zeta-function and the Hurwitz zeta-function with transcendental parameter . In this paper, we obtain a similar theorem on approximation by the shifts , , , where and are absolutely convergent Dirichlet series, and, as , they tend in mean to and respectively. [ABSTRACT FROM AUTHOR]

A discrete universality theorem is obtained in the Voronin sense for the L-functions of elliptic curves. We use the difference of an arithmetical progression h > 0 such that $$ \exp \left\{ {\frac{{2\pi k}} {h}} \right\} $$ is rational for some k ≠ 0. A limit theorem in the space of analytic functions plays a crucial role in the proof. [ABSTRACT FROM AUTHOR]