Explicit Estimates for ζ(s) in the Critical Strip Under the Riemann Hypothesis

Abstract

Abstract Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ to the right of the critical line. As an application we make explicit Titchmarsh’s conditional bound for the Mertens function and Montgomery–Vaughan’s conditional bound for the number of k-free numbers.