Robin's Theorem

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/