Bounding $ζ(s)$ in the critical strip

Emanuel Carneiro; Vorrapan Chandee

doi:10.1016/j.jnt.2010.08.002

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arXiv · 1008.4970

Bounding $ζ(s)$ in the critical strip

Emanuel Carneiro·Vorrapan Chandee

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Abstract

Assuming the Riemann Hypothesis, we make use of the recently discovered \cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\log\left(\tfrac{4 + x^2}{(α-1/2)^2 + x^2}\right)$ to find upper and lower bounds with explicit constants for $\log|ζ(α+ it)|$ in the critical strip, extending the work of Chandee and Soundararajan \cite{CS}.

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Emanuel Carneiro, Vorrapan Chandee. 2010-08-29. Bounding $ζ(s)$ in the critical strip. https://doi.org/10.1016/j.jnt.2010.08.002

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