Crossref Citations
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Axler, Christian
2023.
On Robin’s inequality.
The Ramanujan Journal,
Vol. 61,
Issue. 3,
p.
909.
Published online by Cambridge University Press: 14 August 2017
Robin’s criterion states that the Riemann hypothesis is true if and only if $\unicode[STIX]{x1D70E}(n)<e^{\unicode[STIX]{x1D6FE}}n\log \log n$ for every positive integer $n\geq 5041$. In this paper we establish a new unconditional upper bound for the sum of divisors function, which improves the current best unconditional estimate given by Robin. For this purpose, we use a precise approximation for Chebyshev’s $\unicode[STIX]{x1D717}$-function.