An improved explicit bound on $|\zeta(1/2 + it)|$
  This article proves the bound $|\zeta(\frac{1}{2} + it)|\leq 0.732 t^{\frac{1}{6}} \log t$ for $t \geq 2$, which improves on a result by Cheng and Graham. We also show that $|\zeta(\frac{1}{2}+it)|\leq 0.732 |3.3081+it|^{\frac{1}{6}} \log |3.3081+it|$ for all $t$. 
Dave Platt and Tim Trudgian
math.NT