An Explicit Upper Bound for $|\zeta (1+it)|$

Abstract

In this paper we provide an explicit bound for $|\zeta (1+it)|$ in the form of $|\zeta (1+it)|\le \min \left(\log t,\frac{1}{2}\log t+1.93,\frac{1}{5}\log t+44.02\right)$. This improves on the current best-known explicit bound of $|\zeta (1+it)|\le 62.6(\log t{)}^{2/3}$ up until $t$ of the magnitude $10^{10^7}$.

18 pages