# How plot the Riemann zeta zero spectrum with the Fourier transform? [closed]

In the paper "The Riemann Hypothesis" by J. Brian Conrey in figure 6 there is a plot of the Fourier transform of the error term in the prime number theorem. See the plot to the left in the image below:

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In a blog post called Primes out of Thin Air written by Chris King there is a Matlab program that plots the spectrum. See the plot to the right at the beginning of the post. A translation into Mathematica is possible:

Mathematica:

scale = 10^6;
start = 1;
fin = 50;
its = 490;
xres = 600;
y = N[Accumulate[Table[MangoldtLambda[i], {i, 1, scale}]], 10];
x = scale;
a = 1;
myspan = 800;
xres = 4000;
xx = N[Range[a, myspan, (myspan - a)/(xres - 1)]];
stpval = 10^4;
F = Range[1, xres]*0;

For[t = 1, t <= xres, t++,
For[yy = 0, yy <= Log[x], 1/stpval++,
F[[t]] =
F[[t]] +
Sin[t*myspan/xres*yy]*(y[[Floor[Exp[yy]]]] - Exp[yy])/Exp[yy/2];
]
]
F = F/Log[x];
ListLinePlot[F]


However, this is as I understand it the matrix formulation of the Fourier sine transform and it is therefore very costly to compute. I do NOT recommend running it because it already crashed my computer once.

Is there a way in Mathematica utilising the Fast Fourier Transform, to plot the spectrum with spikes at x-values equal to imaginary part of Riemann zeta zeros?

I have tried the commands "FourierDST" and "Fourier" without success. The problem seems to be that the variable "yy" in the code is included in both "Sin[t*myspan/xres*yy]" and "(y[[Floor[Exp[yy]]]] - Exp[yy])/Exp[yy/2]".

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## closed as off topic by Willie Wong♦Jan 20 '12 at 13:37

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This question might better fit to stackoverflow (it is in its heart numerical and not mathematical). –  Fabian Jan 19 '12 at 21:52
Ok, thank you for the comment. Is there a way to migrate the question or should I rewrite it at stackoverflow? –  Mats Granvik Jan 19 '12 at 21:56
As far as I understand, there is no way to migrate the question. –  Fabian Jan 19 '12 at 21:59
Can't moderators migrate it? –  E.O. Jan 19 '12 at 22:05
SO? This question was made for the new Computational Science site which just went beta. –  Unreasonable Sin Jan 19 '12 at 22:12