In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros σ + i t with 0∞. This can be written more compactly as N(T) = T/(2π) ln(T/(2π e)) + O(ln T). This result was proved by von Mangoldt in 1905 and is hence known as the Riemann-von Mangoldt formula.

Landau's formula | Riemann-Siegel formula | Riemann zeta function | Riemann zeta function zeros