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Fungrim entry: 49704a

(RH)    (Re ⁣(ρn)=12   for all nZ1)\left(\operatorname{RH}\right) \iff \left(\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2} \;\text{ for all } n \in \mathbb{Z}_{\ge 1}\right)
TeX:
\left(\operatorname{RH}\right) \iff \left(\operatorname{Re}\!\left(\rho_{n}\right) = \frac{1}{2} \;\text{ for all } n \in \mathbb{Z}_{\ge 1}\right)
Definitions:
Fungrim symbol Notation Short description
RiemannHypothesisRH\operatorname{RH} Riemann hypothesis
ReRe(z)\operatorname{Re}(z) Real part
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("49704a"),
    Formula(Equivalent(RiemannHypothesis, All(Equal(Re(RiemannZetaZero(n)), Div(1, 2)), ForElement(n, ZZGreaterEqual(1))))))

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2020-04-08 16:14:44.404316 UTC