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Power spectrum of the fluctuation of Chebyshev's prime counting function
The one-sided power spectrum of the fluctuation of Chebyshev's 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/f^2 power
spectrum