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

### 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.author Trudgian, Tim 2014-04-10T05:58:39Z 2014-04-10T05:58:39Z 0004-9727 http://hdl.handle.net/1885/11559 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 $t\leq 10^{2\cdot 10^{5}}$. 6 pages Cambridge University Press http://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 Bulletin of the Australian Mathematical Society 89.2 (2014): 259-264 http://journal.austms.org.au/ojs/index.php/Bulletin/article/view/6826 Zeta function explicit bound A new upper bound for lzeta(1 + it)l Journal article 2014-04-10 http://www.cambridge.org/aus/ Accepted Version Trudgian, Tim, College of Physical and Mathematical Sciences, The Australian National University http://purl.org/au-research/grants/arc/de120100173 ANU Research Publications