The Riemann zeta function and tuning: Difference between revisions
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The expression | The expression | ||
<math>\displaystyle{|\zeta | <math>\displaystyle{\left|\zeta\frac{1}{2} + it)\right|^2 \cdot \overline {\phi(t)}}</math> | ||
is, up to a flip in sign, the Fourier transform of the unnormalized Harmonic Shannon Entropy for <math>N=\infty</math>, where <math>\phi(t)</math> is the characteristic function (aka Fourier transform) of the spreading distribution and <math>\overline {\phi(t)}</math> denotes complex conjugation. | is, up to a flip in sign, the Fourier transform of the unnormalized Harmonic Shannon Entropy for <math>N=\infty</math>, where <math>\phi(t)</math> is the characteristic function (aka Fourier transform) of the spreading distribution and <math>\overline {\phi(t)}</math> denotes complex conjugation. | ||