Extreme values of zeta prime rho

TL;DR

This paper investigates the extreme values of the derivative of the Riemann zeta function at its nontrivial zeros, using Soundararajan's resonance method under the assumption of the Riemann hypothesis.

Contribution

It is the first to apply the resonance method to analyze the extreme values of ta'( ho) assuming the Riemann hypothesis.

Findings

Identifies small and large values of ta'( ho)

Provides bounds for these extreme values

Enhances understanding of the behavior of ta'( ho) at zeros

Abstract

In this article we exhibit small and large values of $\zeta'(\rho)$ by applying Soundararajan's resonance method. Our results assume the Riemann hypothesis.