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Fungrim entry: 9fa2a1

(RH)    (Re(s)=12   for all sC with 0Re(s)1  and  ζ ⁣(s)=0)\left(\operatorname{RH}\right) \iff \left(\operatorname{Re}(s) = \frac{1}{2} \;\text{ for all } s \in \mathbb{C} \text{ with } 0 \le \operatorname{Re}(s) \le 1 \;\mathbin{\operatorname{and}}\; \zeta\!\left(s\right) = 0\right)
\left(\operatorname{RH}\right) \iff \left(\operatorname{Re}(s) = \frac{1}{2} \;\text{ for all } s \in \mathbb{C} \text{ with } 0 \le \operatorname{Re}(s) \le 1 \;\mathbin{\operatorname{and}}\; \zeta\!\left(s\right) = 0\right)
Fungrim symbol Notation Short description
RiemannHypothesisRH\operatorname{RH} Riemann hypothesis
ReRe(z)\operatorname{Re}(z) Real part
CCC\mathbb{C} Complex numbers
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Source code for this entry:
    Formula(Equivalent(RiemannHypothesis, All(Equal(Re(s), Div(1, 2)), ForElement(s, CC), And(LessEqual(0, Re(s), 1), Equal(RiemannZeta(s), 0))))))

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2021-03-15 19:12:00.328586 UTC