Large values of derivatives of the Riemann zeta function on vertical homogeneous progressions

TL;DR

This paper establishes lower bounds for the derivatives of the Riemann zeta function along vertical homogeneous progressions, showing that discrete and continuous cases have similar magnitudes within certain ranges using the resonance method.

Contribution

It introduces new lower bounds for zeta derivatives on vertical progressions and compares discrete and continuous cases with a novel application of the resonance method.

Findings

Lower bounds for derivatives of the Riemann zeta function established

Discrete and continuous cases have similar magnitude within certain ranges

Uses resonance method to achieve results

Abstract

In this paper, we establish lower bounds for the maximum of derivatives of the Riemann zeta function on vertical homogeneous progressions. When the real part $\sigma$ lies within a suitable range, we show that the discrete case has a similar order of magnitude to the continuous case, using the resonance method.