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An improved upper bound for the argument of the Riemann zeta-function on the critical line II

Trudgian, Tim


This paper concerns the function $S(T)$, where $\pi S(T)$ is the argument of the Riemann zeta-function along the critical line. The main result is that \begin{equation*} |S(T)| \leq 0.112\log T + 0.278\log \log T + 2.510, \end{equation*} which holds for all $T\geq e$.

CollectionsANU Research Publications
Date published: 2014-01
Type: Journal article
Source: Journal of Number Theory 134 (2014): 280–292
DOI: 10.1016/j.jnt.2013.07.017


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