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.
Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the q-aspect for the logarithmic derivative (L ′ /L) (σ, χ) of Dirichlet L-functions, where χ is a primitive character modulo q ≥ 10 30 and 1/2 + 1/ log log q ≤ σ ≤ 1 − 1/ log log q. In particular, for σ = 1 we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given.
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