Numerical study of the derivative of the Riemann zeta function at zeros

TL;DR

This paper numerically computes the derivative of the Riemann zeta function at zeros and compares results to known and conjectured asymptotic behaviors.

Contribution

It provides new numerical data on the derivative of the Riemann zeta function at zeros at large heights, testing asymptotic conjectures.

Findings

Numerical data aligns with conjectured asymptotics

Identifies deviations at certain heights

Supports existing hypotheses about zeta function derivatives

Abstract

The derivative of the Riemann zeta function was computed numerically on several large sets of zeros at large heights. Comparisons to known and conjectured asymptotics are presented.