Bounding the log-derivative of the zeta-function

TL;DR

Under the assumption of the Riemann hypothesis, this paper derives explicit bounds for the magnitude of the log-derivative of the Riemann zeta-function within the critical strip, advancing understanding of its behavior.

Contribution

The paper provides the first explicit bounds for the zeta-function's log-derivative in the critical strip assuming the Riemann hypothesis.

Findings

Established explicit bounds for |ζ'/ζ(s)| in the critical strip

Results depend on the validity of the Riemann hypothesis

Enhances understanding of the zeta-function's behavior in critical regions

Abstract

Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann's zeta-function in the critical strip.