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Let a = { a m : m ∈ N } be a periodic multiplicative sequence of complex numbers and L (s ; a) , s = σ + i t a Dirichlet series with coefficients a m . In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 / 2 < σ < 1 via discrete shifts L (s + i h t k ; a) , h > 0 , k ∈ N , where { t k : k ∈ N } is the sequence of Gram points. We prove that the set of such shifts approximating a given analytic function is infinite. This result extends and covers that of [Korolev, M.; Laurinčikas, A. A new application of the Gram points. Aequat. Math. 2019, 93, 859–873]. For the proof, a limit theorem on weakly convergent probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]

In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions. [ABSTRACT FROM AUTHOR]

Let H(D) be the space of analytic functions on the strip D = {σ + it ∈ C : 1/2 < σ < 1}. In this paper, it is proved that there exists a closed non-empty set Fα1,...,αr ⊂ H(D) such that every collection of the functions (f1, . . ., fr) ∈ Fα1,...,αr is approximated by discrete shifts (ζ(s + ikh1, α1), . . ., ζ(s + ikhr, αr)), hj > 0, j = 1, . . ., r, k ∈ N ∪ {0}, of Hurwitz zeta-functions with arbitrary parameters α1, . . ., αr. [ABSTRACT FROM AUTHOR]