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Fungrim entry: 809bc0

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

s \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(s) > 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}(z) 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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2020-04-08 16:14:44.404316 UTC