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 $|\zeta(1/2 + it)| \le 66.7\, t^{27/164}$ for $t \ge 3$. Combined, our results form the sharpest known bounds on $\zeta(1/2 + it)$ for $t \ge \exp(61)$.