Explicit upper and lower bounds on certain functions related to $\hat{I}\P (s)$ for $s>1$

Abstract

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

16 pages