A new upper bound for \(|\zeta(1+it)|\)

T. Trudgian


It is known that \(\zeta(1+ it)\ll (\log t)^{2/3}\) when \(t\gg 1\). This paper provides a new explicit estimate \(|\zeta(1+ it)|\leq \frac{3}{4} \log t\), for \(t\geq 3\). This gives the best upper bound on \(|\zeta(1+ it)|\) for \(t\leq 10^{2\cdot 10^{5}}\).



Riemann zeta function, explicit bound, one line

Remember, for most actions you have to record/upload into OJS
and then inform the editor/author via clicking on an email icon or Completion button.
Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.