Explicit Bound of $|\hat{I}\P \left(1+it\right)|$

Eunice Hoo Qingyi, Lee-Peng Teo

In this work, we show that for all $t\ge e$, \[|ζ(1+it)|\leq 0.6443 \log t. \] The equality is achieved when $t=17.7477$. We also use the Riemann-Siegel formula and numerical com…