Mathematica

Clear[f]

scale = 1000000;

f = Range[scale];

```
```f[[1]] = N@MangoldtLambda[1];

Monitor[Do[

f[[i]] = N@MangoldtLambda[i] + f[[i - 1]], {i, 2, scale}], i]

xres = .004;

xlist = Exp[Range[0, Log[scale - 1], xres]];

tmax = 60;

tres = .015;

s = 1/2;

Monitor[errList1 =

Table[(Total[(xlist^(-1/2 + I t)*(f[[Floor[xlist]]] -

xlist))])*(-1/2 + I t), {t, 0, tmax, tres}];, t]

`Print["Variant of the Fourier transform of the von Mangoldt function"]`

g1 = ListLinePlot[Re[errList1]/Length[xlist], DataRange -> {0, tmax},

PlotRange -> {-.3, 1.3}, Axes -> True, Filling -> Axis];

g2 = Graphics[Line[{{0, 1}, {tmax, 1}}]];

Show[g1, g2, ImageSize -> Large]

Advertisements