Bounding zeta on the 1-line under the partial Riemann hypothesis

Abstract

We provide explicit bounds in the theory of the Riemann zeta-function at the line $\Re s=1$, assuming that the Riemann hypothesis holds until the height $T$. In particular, we improve some bounds, in finite regions, for the logarithmic derivative and the reciprocal of the Riemann zeta-function.

Typos corrected. To appear in the Bulletin of the Australian Mathematical Society