An explicit sub-Weyl bound for $\zeta (1/2+it)$

Abstract

In this article we prove an explicit sub-Weyl bound for the Riemann zeta function $\zeta (s)$ on the critical line $s=1/2+it$. In particular, we show that $|\zeta (1/2+it)|\le 66.7t^{27/164}$ for $t\ge 3$. Combined, our results form the sharpest known bounds on $\zeta (1/2+it)$ for $t\ge \exp (61)$.

30 pages