On Discrete Universality in the Selberg–Steuding Class
Tóm tắt
Let
$ {{\mathcal{S}}} $
be the class of Dirichlet series introduced by Selberg and
modified by Steuding, and let
$ \{\gamma_{k}:k\in{{}}\} $
be
the sequence of the imaginary parts of the nontrivial zeros of the Riemann
zeta-function. Using the modified Montgomery’s pair correlation conjecture, we
prove a universality theorem for a function
$ L(s) $
in
$ {{\mathcal{S}}} $
on approximation of analytic functions by the shifts
$ L(s+ih\gamma_{k}) $
,
$ h>0 $
.
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