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

T. Trudgian

Abstract


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 \(t\leq 10^{2\cdot 10^{5}}\).

10.1017/S0004972713000415

Keywords


Riemann zeta function, explicit bound, one line



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