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Fungrim entry: 809bc0

ζ ⁣(s)ζ ⁣(Re ⁣(s))\left|\zeta\!\left(s\right)\right| \le \zeta\!\left(\operatorname{Re}\!\left(s\right)\right)
Assumptions:sCandRe ⁣(s)>1s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) > 1
TeX:
\left|\zeta\!\left(s\right)\right| \le \zeta\!\left(\operatorname{Re}\!\left(s\right)\right)

s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) > 1
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("809bc0"),
    Formula(LessEqual(Abs(RiemannZeta(s)), RiemannZeta(Re(s)))),
    Variables(s),
    Assumptions(And(Element(s, CC), Greater(Re(s), 1))))

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

2019-08-17 11:32:46.829430 UTC