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

2023/12/15 by Michaela Cully-Hugill, Cully-Hugill, Michaela, Nicol Leong +1
Mathematics · #11M06 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2312.09412

openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide explicit upper bounds of the order log t/loglog 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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