Fungrim entry: 64bd32

\left(\operatorname{RH}\right) \;\implies\; \left(\lambda_{n} \sim \frac{\log(n)}{2} - \frac{\log\!\left(2 \pi\right) + 1 - \gamma}{2}, \; n \to \infty\right)

References:

https://doi.org/10.7169/facm/1317045228

TeX:

\left(\operatorname{RH}\right) \;\implies\; \left(\lambda_{n} \sim \frac{\log(n)}{2} - \frac{\log\!\left(2 \pi\right) + 1 - \gamma}{2}, \; n \to \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`RiemannHypothesis`	$\operatorname{RH}$	Riemann hypothesis
`KeiperLiLambda`	$\lambda_{n}$	Keiper-Li coefficient
`Log`	$\log(z)$	Natural logarithm
`Pi`	$\pi$	The constant pi (3.14...)
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("64bd32"),
    Formula(Implies(RiemannHypothesis, AsymptoticTo(KeiperLiLambda(n), Sub(Div(Log(n), 2), Div(Sub(Add(Log(Mul(2, Pi)), 1), ConstGamma), 2)), n, Infinity))),
    References("https://doi.org/10.7169/facm/1317045228"))

Topics using this entry

Keiper-Li coefficients