A new bound for the error term in the approximate functional equation for the derivatives of the Hardy's Z-function

TL;DR

This paper introduces a significantly improved bound for the error term in the approximate functional equation related to derivatives of Hardy's Z-function, especially effective for high-order derivatives.

Contribution

The paper presents a new, tighter bound for the error term in the approximate functional equation for Hardy's Z-function derivatives, surpassing previous bounds for high orders.

Findings

New bound is significantly better for high-order derivatives

Improves upon previous uniform bounds by Lavrik and the author

Enhances accuracy of functional equation approximations

Abstract

Lavrik and the author gave uniform bounds of the error term in the approximate functional equation for the derivatives of the Hardy's Z-function. We obtain a new bound of this error term which is much better for high order derivatives.