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arXiv · 2607.08342

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

Stephan Ramon Garcia·Loïc Grenié·Giuseppe Molteni
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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 $(\zeta'/\zeta)(s)$.

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Stephan Ramon Garcia, Loïc Grenié, Giuseppe Molteni. 2026-07-09. Explicit upper and lower bounds on certain functions related to $\zeta(s)$ for $s>1$. https://arxiv.org/abs/2607.08342

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