An explicit sub-Weyl bound for ζ(1/2 + it)

Abstract

In this article we prove an explicit sub-Weyl bound for the Riemann zeta function ζ(s) on the critical line s=1/2+it. In particular, we show that |ζ(1/2+it)|≤66.7t27/164 for t≥3. Combined, our results form the sharpest known bounds on ζ(1/2+it) for t≥exp⁡(61).