New results for witnesses of Robin’s criterion

Saouter, Yannick

doi:10.1090/mcom/3687

New results for witnesses of Robin’s criterion
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by Yannick Saouter;

Math. Comp. 91 (2022), 909-920

DOI: https://doi.org/10.1090/mcom/3687

Published electronically: October 15, 2021

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Abstract:

In a seminal paper, Robin proved that the Riemann hypothesis holds if and only if the inequality $\sigma (n)=\sum _{d|n} d < e^\gamma n \log \log n$ holds for all integers greater than 5040, where $\gamma$ is the Euler-Mascheroni constant. In this article, we prove new results on putative violations of Robin’s criterion.

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