Robin’s theorem
Let be the sum of the positive divisors of an integer and
The Riemann Hypothesis is true if and only if
where is the Euler–Mascheroni constant.
References
- 1 G. Robin: Grandes valeurs de la fonction somme des diviseurs et hypothèse deRiemann. J. Math. Pures Appl. 14 (1984) 187–213.
- 2 J. C. Lagarias: An elementary problem equivalent
to the Riemann hypothesis. Amer. Math. Monthly 109 (2002), 534–543. Available at http://arxiv.org/abs/math/0008177