User:Manishkrisna108/sandbox

welcome in the world of SANDS.

Lots of messy objets are here and there.In this page I am supposed to use letters and numbers as sand to construct models before wiki editing. somatic

Approximation by Riemann zeta zeros
{wb:Fundamentals of Physics}

The real part of the sum over the zeta zeros:
 * $$-\sum_{i=1}^{\infty} n^{\rho(i)} $$, where $ρ(i)$ is the $i$-th zeta zero, peaks at primes, as can be seen in the adjoining graph, and can also be verified through numerical computation. It does not sum up to the Von Mangoldt function.

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