Universality results for the Riemann
zeta-function
Antanas Laurinčikas (Vilnius)
Abstract: In 1975, S. M. Voronin proved that the Riemann zeta-function
ζ(s) is universal in the sense that any analytic function can be approximated
with a given accuracy uniformly on compact subsets of the critical strip by
shifts ζ(s + iτ ), τ ∈ R. In the paper, we present a short survey on the
Voronin theorem. The main attention is devoted to effectivization problem
of the universality theorem as well as to the universality of F (ζ(s)) for some
classes of functions F .
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