Lower bound for the maximum of some derivative of Hardy's function

TL;DR

This paper establishes a lower bound for the maximum of certain derivatives of Hardy's function, leveraging the distribution of zeros of the zeta function under the Riemann hypothesis.

Contribution

It introduces a novel approach to bounding derivatives of Hardy's function using zero distribution assumptions.

Findings

Derived a new lower bound for derivatives of Hardy's function

Connected zero distribution of zeta function to Hardy's function behavior

Assumed Riemann hypothesis for theoretical results

Abstract

Under the Riemann hypothesis, we use the distribution of zeros of the zeta function to get a lower bound for the maximum of some derivative of Hardy's function.