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

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

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