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Fungrim entry: 3142ec

(RH)    (σ1 ⁣(n)<eγnlog ⁣(log(n))   for all nZ5041)\left(\operatorname{RH}\right) \iff \left(\sigma_{1}\!\left(n\right) < {e}^{\gamma} n \log\!\left(\log(n)\right) \;\text{ for all } n \in \mathbb{Z}_{\ge 5041}\right)
TeX:
\left(\operatorname{RH}\right) \iff \left(\sigma_{1}\!\left(n\right) < {e}^{\gamma} n \log\!\left(\log(n)\right) \;\text{ for all } n \in \mathbb{Z}_{\ge 5041}\right)
Definitions:
Fungrim symbol Notation Short description
RiemannHypothesisRH\operatorname{RH} Riemann hypothesis
DivisorSigmaσk ⁣(n)\sigma_{k}\!\left(n\right) Sum of divisors function
Expez{e}^{z} Exponential function
ConstGammaγ\gamma The constant gamma (0.577...)
Loglog(z)\log(z) Natural logarithm
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("3142ec"),
    Formula(Equivalent(RiemannHypothesis, All(Less(DivisorSigma(1, n), Mul(Mul(Exp(ConstGamma), n), Log(Log(n)))), ForElement(n, ZZGreaterEqual(5041))))))

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2020-08-27 09:56:25.682319 UTC