An improved explicit estimate for $\zeta(1/2+it)$

TL;DR

This paper presents an improved explicit subconvex bound for the Riemann zeta function on the critical line, correcting previous errors and achieving a better explicit estimate for its magnitude.

Contribution

The paper corrects a previous mistake in the Kusmin-Landau lemma and provides an improved explicit bound for (1/2+it), advancing the understanding of the zeta function's behavior.

Findings

Recovered and improved the explicit bound for |(1/2+it)|

Corrected the Kusmin-Landau lemma used in prior bounds

Established a more accurate estimate for the zeta function on the critical line

Abstract

An explicit subconvex bound for the Riemann zeta function $\zeta(s)$ on the critical line $s=1/2+it$ is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction in that lemma, we recover and improve the record explicit bound for $|\zeta(1/2 + it)|$.