An improved explicit bound on $|\zeta(1/2 + it)|$

Dave Platt; Tim Trudgian

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arXiv · 1402.3953

An improved explicit bound on $|\zeta(1/2 + it)|$

Dave Platt·Tim Trudgian

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Abstract

This article proves the bound $|\zeta(\frac{1}{2} + it)|\leq 0.732 t^{\frac{1}{6}} \log t$ for $t \geq 2$, which improves on a result by Cheng and Graham. We also show that $|\zeta(\frac{1}{2}+it)|\leq 0.732 |3.3081+it|^{\frac{1}{6}} \log |3.3081+it|$ for all $t$.

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Dave Platt, Tim Trudgian. 2014-02-17. An improved explicit bound on $|\zeta(1/2 + it)|$. https://arxiv.org/abs/1402.3953

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