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- W4300628885 abstract "In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $sigma(n)<e^gamma nloglog n$ holds for every integer $n>5040$, where $sigma(n)$ is the sum of divisors function, and $gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets $cS$ of the natural numbers such that the Robin inequality holds for all but finitely many $nincS$. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/phi(n)<e^{gamma}log log n$; since $sigma(n)/n<n/phi(n)$ for $n>1$ our results for the Robin inequality follow at once." @default.
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- W4300628885 date "2007-10-12" @default.
- W4300628885 modified "2023-09-28" @default.
- W4300628885 title "The Nicolas and Robin inequalities with sums of two squares" @default.
- W4300628885 doi "https://doi.org/10.48550/arxiv.0710.2424" @default.
- W4300628885 hasPublicationYear "2007" @default.
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