A new upper bound for lzeta(1 + it)l
Tim Trudgian · ANU Open Research (Australian National University) · 2014
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 $t\\leq 10^{2\\cdot 10^{5}}$.