Extreme values of the Riemann zeta function at its critical points in the critical strip

TL;DR

This paper investigates the extreme magnitudes of the Riemann zeta function at its critical points within the critical strip, providing estimates for large and small values in a specific region.

Contribution

It offers new estimates for the values of |z( ho')| at critical points where z'( ho')=0 in the right half of the critical strip, a region less explored in prior research.

Findings

Estimates for large values of |z( ho')|

Estimates for small values of |z( ho')|

Analysis focused on critical points with 1/2<Re( ho')<1

Abstract

We estimate large and small values of $|\zeta(\rho')|$, where $\rho'$ runs over critical points of the zeta function in the right half of the critical strip, that is, the points where $\zeta'(\rho')=0$ and $1/2<\Re \rho'<1$.