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

Collections ANU Research Publications 2014-04-10 Journal article http://hdl.handle.net/1885/11559 Bulletin of the Australian Mathematical Society 89.2 (2014): 259-264