Robin's theorem, proved by Guy Robin in 1984, states that the inequality sigma(n) is less than e to the Euler-Mascheroni constant times n times the natural logarithm of the natural logarithm of n holds for all sufficiently large n if and only if the Riemann hypothesis is true, where sigma(n) is the sum of divisors of n. The inequality traces back to a 1915 conjecture of Ramanujan made under the assumption of the Riemann hypothesis. Because the theorem provides an elementary reformulation of the Riemann hypothesis in terms of the divisor-sum function, it offers a route to testing the hypothesis directly by calculation: a single integer greater than 5040 that violates the inequality would disprove the Riemann hypothesis. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Statement FormCharacterization Theorem 1 Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Divisor function (Wikipedia)
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1. Divisor function (Wikipedia)
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In 1984, Guy Robin proved that the inequality is true for all n > 5040 if and only if the Riemann hypothesis is true.
In Branch: Number Theory, Lead sentence
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an inte
View the SourceRobin's theorem (Wikipedia)
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