Fungrim entry: 3142ec

\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
`RiemannHypothesis`	$\operatorname{RH}$	Riemann hypothesis
`DivisorSigma`	$\sigma_{k}\!\left(n\right)$	Sum of divisors function
`Exp`	${e}^{z}$	Exponential function
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`Log`	$\log(z)$	Natural logarithm
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	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))))))

Topics using this entry

Riemann hypothesis

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC