BOUNDING ZETA ON THE 1-LINE UNDER THE PARTIAL RIEMANN HYPOTHESIS

Abstract We provide explicit bounds for the Riemann zeta-function on the line

$\mathrm {Re}\,{s}=1$

, assuming that the Riemann hypothesis holds up to height T. In particular, we improve some bounds in finite regions for the logarithmic derivative and the reciprocal of the Riemann zeta-function.