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Abstract
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For a fixed
,
an
-point
of the Riemann zeta-function is a complex number
such
that
.
Recently J. Steuding estimated the sum
for a fixed
as
, and used this to prove that
the ordinates
are uniformly
distributed modulo
.
We provide uniform estimates for this sum when
and
, and
.
Using this, we bound the discrepancy of the sequence
when
. We
also find explicit representations and bounds for the Dirichlet coefficients of the series
and
upper bounds for the abscissa of absolute convergence of this series.
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Keywords
Riemann zeta-function, $a$-points, uniform distribution,
discrepancy
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Mathematical Subject Classification 2010
Primary: 11M06, 11M26
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Milestones
Received: 7 January 2019
Revised: 5 May 2019
Accepted: 14 May 2019
Published: 21 December 2019
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