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Abstract
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We continue our investigations regarding the distribution of positive and negative values of
Hardy’s
-functions
in the interval
when the
conductor
and
both tend to infinity.
We show that for
,
,
with
,
satisfying
, the Lebesgue measure
of the set of values of
for which
is
as
,
where
denotes the number of distinct prime factors of the conductor
of the
character
, and
is the usual Euler totient.
This improves upon our earlier result. We also include a corrigendum for the first part of this article.
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Keywords
Hardy's function, Hardy–Selberg function, Dirichlet
$L$-function, value distribution
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Mathematical Subject Classification 2010
Primary: 11M06, 11M26
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Milestones
Received: 10 November 2018
Revised: 7 May 2019
Accepted: 31 May 2019
Published: 23 July 2019
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