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A new upper bound for lzeta(1 + it)l

Trudgian, Tim

Description

It is known that $\zeta(1+ it)\ll (\log t)^{2/3}$ when $t\gg 1$. This paper provides a new explicit estimate \ $|\zeta(1+ it)|\leq \frac{3}{4} \log t$, for $t\geq 3$. This gives the best upper bound on $|\zeta(1+ it)|$ for $t\leq 10^{2\cdot 10^{5}}$.

dc.contributor.authorTrudgian, Tim
dc.date.accessioned2014-04-10T05:58:39Z
dc.date.available2014-04-10T05:58:39Z
dc.identifier.issn0004-9727
dc.identifier.urihttp://hdl.handle.net/1885/11559
dc.description.abstractIt is known that $\zeta(1+ it)\ll (\log t)^{2/3}$ when $t\gg 1$. This paper provides a new explicit estimate \ $|\zeta(1+ it)|\leq \frac{3}{4} \log t$, for $t\geq 3$. This gives the best upper bound on $|\zeta(1+ it)|$ for $t\leq 10^{2\cdot 10^{5}}$.
dc.format6 pages
dc.publisherCambridge University Press
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0004-9727/author can archive pre-print (ie pre-refereeing); author can archive post-print (ie final draft post-refereeing); subject to 12 month embargo, author can archive publisher's version/PDF
dc.sourceBulletin of the Australian Mathematical Society 89.2 (2014): 259-264
dc.source.urihttp://journal.austms.org.au/ojs/index.php/Bulletin/article/view/6826
dc.subjectZeta function
dc.subjectexplicit bound
dc.titleA new upper bound for lzeta(1 + it)l
dc.typeJournal article
dc.date.issued2014-04-10
local.publisher.urlhttp://www.cambridge.org/aus/
local.type.statusAccepted Version
local.contributor.affiliationTrudgian, Tim, College of Physical and Mathematical Sciences, The Australian National University
dc.relationhttp://purl.org/au-research/grants/arc/de120100173
CollectionsANU Research Publications

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