# 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))))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC