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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 $t\leq 10^{2\cdot 10^{5}}$.

CollectionsANU Research Publications
Date published: 2014-04-10
Type: Journal article
URI: http://hdl.handle.net/1885/11559
Source: Bulletin of the Australian Mathematical Society 89.2 (2014): 259-264

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