Fungrim entry: a78abc

\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C},\,0 \le \operatorname{Re}(s) \le 1} \zeta\!\left(s\right) = \left\{ \rho_{n} : n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \ne 0 \right\}

TeX:

\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C},\,0 \le \operatorname{Re}(s) \le 1} \zeta\!\left(s\right) = \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
`Re`	$\operatorname{Re}(z)$	Real part
`RiemannZetaZero`	$\rho_{n}$	Nontrivial zero of the Riemann zeta function
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("a78abc"),
    Formula(Equal(Zeros(RiemannZeta(s), ForElement(s, CC), LessEqual(0, Re(s), 1)), Set(RiemannZetaZero(n), For(n), And(Element(n, ZZ), NotEqual(n, 0))))))

Fungrim entry: a78abc

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