Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function

Tim Trudgian

doi:10.7169/facm/2015.52.2.5

June 2015 Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function

Tim Trudgian

Funct. Approx. Comment. Math. 52(2): 253-261 (June 2015). DOI: 10.7169/facm/2015.52.2.5

Abstract

The purpose of this article is consider $|\zeta'(\sigma + it)/\zeta(\sigma + it)|$ and $|\zeta(\sigma + it)|^{-1}$ when $\sigma$ is close to unity. We prove that $|\zeta'(\sigma + it)/\zeta(\sigma + it)| \leq 87\log t$ and $|\zeta(\sigma + it)|^{-1} \leq 6.9\times 10^{6} \log t$ for $\sigma \geq 1-1/(8 \log t)$ and $t\geq 45$.

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Tim Trudgian "Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function," Functiones et Approximatio Commentarii Mathematici 52(2), 253-261, (June 2015). https://doi.org/10.7169/facm/2015.52.2.5

Published: June 2015

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