May 9, 2024Journal of Mathematical Analysis and ApplicationsOpen Access

Explicit estimates for the Riemann zeta function close to the 1-line

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Abstract

We provide explicit upper bounds of the order log⁡t/log⁡log⁡t for |ζ′(s)/ζ(s)| and |1/ζ(s)| when σ is close to 1. These improve existing bounds for ζ(s) on the 1-line.

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Cully-Hugill et al. (2024) studied this question.

synapsesocial.com/papers/68e6ada0b6db64358762fa87 https://doi.org/10.1016/j.jmaa.2024.128494

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Abstract

We provide explicit upper bounds of the order log⁡t/log⁡log⁡t for |ζ′(s)/ζ(s)| and |1/ζ(s)| when σ is close to 1. These improve existing bounds for ζ(s) on the 1-line.

Explicit estimates for the Riemann zeta function close to the 1-line

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Explicit estimates for the Riemann zeta function close to the 1-line

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