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

Abstract

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

5 pages

References in corpus (1)

• An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Cited by in corpus (1)

• An explicit upper bound for Siegel zeros of imaginary quadratic fields