Sharp lower bounds for moments of $\zeta'(\rho)$

TL;DR

This paper establishes precise lower bounds for the moments of the derivative of the Riemann zeta-function at its zeros, assuming the Riemann hypothesis, advancing understanding of zeta function behavior.

Contribution

It provides sharp lower bounds for the moments of ta'( ho) for all real k , under RH, filling a gap in the understanding of zeta function derivatives.

Findings

Sharp lower bounds for moments of ta'( ho) for all real k 

Results hold under the Riemann hypothesis

Advances the theoretical understanding of zeta function derivatives

Abstract

We study the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros to establish sharp lower bounds for all real $k \geq 0$ under the Riemann hypothesis (RH).