Lower bounds for negative moments of $\zeta'(\rho)$

TL;DR

This paper derives lower bounds for the negative moments of the derivative of the Riemann zeta function at its zeros, assuming RH and simple zeros, advancing understanding of the zeta function's behavior.

Contribution

It provides the first lower bounds for negative moments of z derivative at zeros under RH and simplicity assumptions.

Findings

Established lower bounds for negative moments of z'() at zeros.

Results hold for all negative moments with k<0.

Assumes RH and all zeros are simple.

Abstract

We establish lower bounds for the discrete $2k$-th moment of the derivative of the Riemann zeta function at nontrivial zeros for all $k<0$ under the Riemann hypothesis (RH) and the assumption that all zeros of $\zeta(s)$ are simple.