 Riemann–von Mangoldt explicit formula

ID: riemann-von-mangoldt-explicit-formula

For

x > 1

away from a jump of

ψ

ψ (x) = x - \sum_{ρ} \frac{x ^{ρ}}{ρ} - lo g (2 π) - \frac{1}{2} lo g (1 - x^{- 2}),

where the sum over Nontrivial zeros of the Riemann zeta function is taken symmetrically. A finite-height version has an explicit truncation error controlled by

x / T

and the distance from

x

to the nearest prime power.

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