An improved explicit bound on vertical bar zeta(1/2+it)vertical bar

摘要

This article proves the bound vertical bar zeta(1/2 + it)vertical bar <= 0.732t (1/6) log t for t >= 2, which improves on a result by Cheng and Graham. We also show that vertical bar zeta(1/2 + it)vertical bar <= 0.732 vertical bar 4.678 + it vertical bar(1/6) log vertical bar 4.678 + it vertical bar for all t. (C) 2014 Elsevier Inc. All rights reserved.