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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 theorem is obtained on the approximation of a collection of analytic functions in short intervals by a collection of shifts of the Riemann zeta-function , where are algebraic numbers linearly independent over the field of rational numbers. [ABSTRACT FROM AUTHOR]

A theorem dealing with the approximation of analytic functions in the strip by shifts of an absolutely convergent Dirichlet series close to a periodic zeta- function with multiplicative coefficients is proved. [ABSTRACT FROM AUTHOR]

We prove that every collection of analytic functions (f1(s),... , fr(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions (ζ(s + iγκh, α1), ... , ζ(s + iγκh, αr)), h > 0, where 0 < γ1 ≤ γ2 ≤ ... are the imaginary parts of nontrivial zeros of the Riemann zeta-function ζ(s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over ℚ of the set {log(m + αj) : m ∈ ℕ0, j = 1, ... , r}. [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]