4.5 $J[x]$: Riemann’s Prime-Power Counting Function

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The following three plots illustrate the Fourier series for Riemann’s prime-power counting function $J[x]$ (blue) evaluated at $f={1, 2, 3}$. The $Li[x]$ function (gray) is shown as a reference.

Fourier Series for j[x] Evaluated at f=1.
$J[x]$ evaluated at $f=1$.
Fourier Series for j[x] Evaluated at f=2.
$J[x]$ evaluated at $f=2$.
Fourier Series for j[x] Evaluated at f=3.
$J[x]$ evaluated at $f=3$.