Abstract
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.
Publisher
Cambridge University Press (CUP)
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