Abstract
Let H(D) be the space of analytic functions on the strip ... In this paper, it is proved that there exists a closed non-empty set ...such that every collection of the functions ... is approximated by discrete shifts .., of Hurwitz zeta-functions with arbitrary parameters ...
Highlights
Let s = σ + it be a complex variable, and α, 0 < α 1, be a fixed parameter
Universality results for the function ζ(s, α) follows from the Mishou theorem on the joint universality of the Riemann and Hurwitz zeta-functions
In [8], the following joint approximation theorem for Hurwitz zeta-functions has been proved
Summary
For every ε > 0, lim inf meas τ ∈ [0, T ] : sup |ζ(s + iτ, α) − f (s)| < ε > 0 Different proofs of the latter inequality are given in [1, 10, 36] and [28]. Universality results for the function ζ(s, α) follows from the Mishou theorem on the joint universality of the Riemann and Hurwitz zeta-functions. There are known several results of approximation of analytic functions by shifts of the functions ζ(s, α) and ζ(s, α; a) with algebraic irrational parameter α, the set of approximated functions is not identified. In [8], the following joint approximation theorem for Hurwitz zeta-functions has been proved. It will be proved that the set Fα,h is the support of a certain Hr(D)-valued random element
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