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

Abstract

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