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Fungrim entry: 692e42

zerossCζ(s)={2n:nZ1}{ρn:nZandn0}\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C}} \zeta(s) = \left\{ -2 n : n \in \mathbb{Z}_{\ge 1} \right\} \cup \left\{ \rho_{n} : n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0 \right\}
TeX:
\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C}} \zeta(s) = \left\{ -2 n : n \in \mathbb{Z}_{\ge 1} \right\} \cup \left\{ \rho_{n} : n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0 \right\}
Definitions:
Fungrim symbol Notation Short description
ZeroszerosxSf(x)\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x) Zeros (roots) of function
RiemannZetaζ(s)\zeta(s) Riemann zeta function
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("692e42"),
    Formula(Equal(Zeros(RiemannZeta(s), ForElement(s, CC)), Union(Set(Neg(Mul(2, n)), ForElement(n, ZZGreaterEqual(1))), Set(RiemannZetaZero(n), For(n), And(Element(n, ZZ), Unequal(n, 0)))))))

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2019-10-05 13:11:19.856591 UTC