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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 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]