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

Stephan Ramon Garcia; Loïc Grenié; Giuseppe Molteni

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

Number Theory 2026-07-09 v1

Authors: Stephan Ramon Garcia , Loïc Grenié , Giuseppe Molteni

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 $(\zeta'/\zeta)(s)$ .

Keywords

Riemann zeta function explicit bounds derivatives logarithmic derivative analytic number theory

Cite

@article{arxiv.2607.08342,
  title  = {Explicit upper and lower bounds on certain functions related to $ζ(s)$ for $s>1$},
  author = {Stephan Ramon Garcia and Loïc Grenié and Giuseppe Molteni},
  journal= {arXiv preprint arXiv:2607.08342},
  year   = {2026}
}

Comments

16 pages