Explicit upper and lower bounds on certain functions related to $ζ(s)$ for $s>1$

Abstract

We provide explicit upper and lower bounds for certain commonly occurring expressions that involve the Riemann zeta function $ζ(s)$ and its derivatives on $s>1$. For example, this improves upon existing bounds for $(s-1)ζ(s)$ and its derivatives, and for $(ζ'/ζ)(s)$.