An improved explicit bound on $|ζ(1/2 + it)|$

Abstract

This article proves the bound $|ζ(\frac{1}{2} + it)|\leq 0.732 t^{\frac{1}{6}} \log t$ for $t \geq 2$, which improves on a result by Cheng and Graham. We also show that $|ζ(\frac{1}{2}+it)|\leq 0.732 |3.3081+it|^{\frac{1}{6}} \log |3.3081+it|$ for all $t$.

9 pages; to appear in J. Number Theory