An improved explicit bound on $|\hat{I}\P (1/2+it)|$

Abstract

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

9 pages; to appear in J. Number Theory