A note on the large values of $|\zeta^{(\ell)}(1+{\rm i}t)|$

TL;DR

This paper studies the extreme magnitudes of derivatives of the Riemann zeta function along the 1-line, providing improved lower bounds for their maximum values over large intervals.

Contribution

It offers a larger lower bound for the maximum of the derivatives of (s) on the 1-line, advancing previous results by Yang.

Findings

Established a larger lower bound for ^{(\u03bb)}(1+it) maxima

Improved understanding of the size of zeta derivatives on the 1-line

Enhanced previous bounds by Yang

Abstract

We investigate the large values of the derivatives of the Riemann zeta function $\zeta(s)$ on the 1-line. We give a larger lower bound for $\max_{t\in[T,2T]}|\zeta^{(\ell)}(1+{\rm i} t)|$, which improves the previous result established by Yang.