Von Mangoldt Function - Approximation By Riemann Zeta Zeros

Approximation By Riemann Zeta Zeros

The real part of the sum over the zeta zeros:

approximates the von Mangoldt function by summing several waves onto each other (page 346).

The Fourier transform of the von Mangoldt function gives a spectrum with spikes at ordinata equal to imaginary part of the Riemann zeta function zeros. This is sometimes called a duality.