A modest improvement on the function $S(T)$

TL;DR

This paper presents a modest enhancement to the explicit bounds on the growth of the function S(T), highlighting potential for larger improvements with better bounds on the zeta function's magnitude.

Contribution

It provides a slight improvement on existing bounds for S(T) and discusses how stronger bounds on |z(1/2+it)| could lead to more significant advances.

Findings

Improved explicit bounds on S(T) are achieved.

Better bounds on |z(1/2+it)| could significantly enhance results.

The paper suggests pathways for future improvements.

Abstract

This paper contains a small improvement to the explicit bounds on the growth of the function $S(T)$. It is shown how more substantial improvements are possible if one has better explicit bounds on the growth of $|\zeta(\frac{1}{2}+it)|$.