Fungrim entry: bfaeb5

\left(\operatorname{RH}\right) \iff \left(\left|\pi(x) - \operatorname{li}(x)\right| < \sqrt{x} \log(x) \;\text{ for all } x \in \left[2, \infty\right)\right)

References:

https://mathoverflow.net/q/338066

TeX:

\left(\operatorname{RH}\right) \iff \left(\left|\pi(x) - \operatorname{li}(x)\right| < \sqrt{x} \log(x) \;\text{ for all } x \in \left[2, \infty\right)\right)

Definitions:

Fungrim symbol	Notation	Short description
`RiemannHypothesis`	$\operatorname{RH}$	Riemann hypothesis
`Abs`	$\left\|z\right\|$	Absolute value
`PrimePi`	$\pi(x)$	Prime counting function
`LogIntegral`	$\operatorname{li}(z)$	Logarithmic integral
`Sqrt`	$\sqrt{z}$	Principal square root
`Log`	$\log(z)$	Natural logarithm
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("bfaeb5"),
    Formula(Equivalent(RiemannHypothesis, All(Less(Abs(Sub(PrimePi(x), LogIntegral(x))), Mul(Sqrt(x), Log(x))), ForElement(x, ClosedOpenInterval(2, Infinity))))),
    References("https://mathoverflow.net/q/338066"))

Topics using this entry

Riemann hypothesis