Joint discrete universality for periodic zeta-functions

Joint Discrete Approximation of a Pair of Analytic Functions by Periodic Zeta-Functions

“…Similar results also are given in [17] and [19]. Approximation results for more general collections consisting from periodic zeta functions were obtained in [3,11,12,13,14,16,20] and [23].…”

On Discrete Value Distribution of Certain Compositions

“…Let s = σ + it be a complex variable, and a = {a m : m ∈ N} be a periodic sequence of complex numbers with minimal period k ∈ N. The periodic zetafunction ζ(s; a) is defined, for σ > 1, by the Dirichlet series This note is devoted to discrete value distribution of collections consisting of periodic and periodic Hurwitz zeta-functions. In [2], the approximation of a collection of analytic functions by discrete shifts of the above collections of zeta-functions has been considered. For j = 1, .…”

Joint universality of periodic zeta-functions with multiplicative coefficients

“…was required, however, it can be easily removed. Joint universality of more general collections of zeta-functions was studied in [12,14,16,17] and [7][8][9]. We note that joint mixed universality theorems imply those for zetafunction with Euler product.…”