I post a question generating Riemann Zeta zero spectrum using Mathematica on board of mathematica.stackexchange.com:
Can anyone help ?
It is related to a plot of paper "The Riemann Hypothesis" by J. Brian Conrey: the Fourier transform of the error term in the prime number theorem.
Beside Mathematica problems, I also have questions regarding the math behind it:
A: Do we do Fourier analysis on Chebyshev function itself or the error term, (Chebyshev - x) ?
B: Why do we need to calculate 10^6 points of Chebyshev function for this purpose ? Can we do with some less points, such as: 10^4 ?
C: How is the number of data points for Chebyshev function related to the resolution of frequency domain of zero spectrum ?
D: Can we use built Fast Fourier Transform to do above analysis or do we have to implement discrete sine transform ourselves as in the code.