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

Andrés Chirre

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

Number Theory 2023-11-21 v2

Authors: Andrés Chirre

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.

Keywords

riemann zeta-function partial riemann hypothesis explicit bounds logarithmic derivative 1-line

Cite

@article{arxiv.2310.06723,
  title  = {Bounding zeta on the 1-line under the partial Riemann hypothesis},
  author = {Andrés Chirre},
  journal= {arXiv preprint arXiv:2310.06723},
  year   = {2023}
}

Comments

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

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