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# Fungrim entry: 692e42

$\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C}} \zeta\!\left(s\right) = \left\{ -2 n : n \in \mathbb{Z}_{\ge 1} \right\} \cup \left\{ \rho_{n} : n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0 \right\}$
TeX:
\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C}} \zeta\!\left(s\right) = \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
Zeros$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$ Zeros (roots) of function
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
RiemannZetaZero$\rho_{n}$ Nontrivial zero of the Riemann zeta function
ZZ$\mathbb{Z}$ 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), NotEqual(n, 0)))))))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC