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Fungrim entry: 49704a

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

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2019-08-21 11:44:15.926409 UTC