An Explicit Upper Bound for $|\zeta(1+it)|$

Dhir Patel

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arXiv · 2009.00769

An Explicit Upper Bound for $|\zeta(1+it)|$

Dhir Patel

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Abstract

In this paper we provide an explicit bound for $|\zeta(1+it)|$ in the form of $|\zeta(1+it)|\leq \min\left(\log t, \frac{1}{2}\log t+1.93, \frac{1}{5}\log t+44.02 \right)$. This improves on the current best-known explicit bound of $|\zeta(1+it)|\leq 62.6(\log t)^{2/3}$ up until $t$ of the magnitude $10^{10^7}$.

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Dhir Patel. 2020-09-02. An Explicit Upper Bound for $|\zeta(1+it)|$. https://arxiv.org/abs/2009.00769

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