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

Abstract

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

arXiv comment19 pages