Power spectrum of the fluctuation of Chebyshevʹs prime counting function

The one-sided power spectrum of the fluctuation of Chebyshevʹs weighted prime counting function is numerically estimated based on samples of the fluctuating function of different sizes. The power spectrum is also estimated analytically for large frequency based on Riemann hypothesis and the exact formula for the fluctuating function in terms of all the non-trivial Riemann zeroes. Our analytical estimate is consistent with our numerical estimate of a 1/f2 power spectrum.