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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 $(ζ'/ζ)(s)$.
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BibTeX
@misc{garcia2026explicit,
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},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.08342},
eprint = {2607.08342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.08342},
}
RIS
TY - UNPB
TI - Explicit upper and lower bounds on certain functions related to ζ(s) for s>1
AU - Stephan Ramon Garcia
AU - Loïc Grenié
AU - Giuseppe Molteni
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.08342
UR - https://arxiv.org/abs/2607.08342
AB - 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 $(ζ'/ζ)(s)$.
ER -