• 1 Tata Institute for Fundamental Research

In the previous paper in this series, we proved a lower bound for $f(H)=\min_{T\geq1}\max_{T\leq t\leq T+H}\vert(\zeta(1+it))^z\vert,$ where $z=\exp(i\theta)$ and $0\leq\theta<2\pi$. In this paper, we prove an upper bound for $f(H)$ and present some applications.