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单词 RobinsTheorem
释义

Robin’s theorem


Let σ(n) be the sum of the positive divisorsMathworldPlanetmathPlanetmath of an integer n and

G(n):=σ(n)nln(lnn)  (n= 2, 3, 4,).

The Riemann HypothesisMathworldPlanetmath is true if and only if

G(n)<eγfor all n> 7!

where γ 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 equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the Riemann hypothesis.  - Amer. Math. Monthly 109 (2002), 534–543. Available at http://arxiv.org/abs/math/0008177
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