Fungrim home page

Fungrim entry: a78abc

zerossC,0Re(s)1ζ(s)={ρn:nZandn0}\mathop{\operatorname{zeros}\,}\limits_{s \in \mathbb{C},\,0 \le \operatorname{Re}(s) \le 1} \zeta(s) = \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(s) = \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
ReRe(z)\operatorname{Re}(z) Real part
RiemannZetaZeroρn\rho_{n} Nontrivial zero of the Riemann zeta function
ZZZ\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), Unequal(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.

2019-10-05 13:11:19.856591 UTC