A new improved explicit estimate for $\zeta\left( 1/2+it\right)$

TL;DR

This paper introduces an improved explicit subconvexity bound for the Riemann zeta function along the critical line, combining refined analytic techniques with computational methods to advance understanding of its behavior.

Contribution

It provides a new, sharper explicit bound for ta(s) on the critical line, improving previous results through a refined van der Corput method and computational verification.

Findings

New explicit subconvexity bound for ta(1/2+it)

Enhanced analytic techniques combined with computational calculations

Sharper estimates compared to previous bounds

Abstract

In this paper, we present an improved explicit subconvexity result for the Riemann zeta function $\zeta\left( s\right)$ along the critical line $s=1/2+it$, given by Hiary, Patel and Yang in 2024. This new bound is derived by combining a refined, explicit version of the van der Corput method together with computational calculations.