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

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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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-12, Vol.540 (2), p.128494, Article 128494
Main Authors: Cully-Hugill, Michaela, Leong, Nicol
Format: Article
Language:English
Subjects:
Explicit estimates
Logarithmic derivative of zeta
Reciprocal of zeta
Riemann zeta function
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Summary: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.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128494