The Riemann zeta function and tuning: Difference between revisions
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<math>\displaystyle F_s(x) = \Re \ln \zeta\left(s + \frac{2 \pi i}{\ln 2}x\right)</math> | <math>\displaystyle F_s(x) = \Re \ln \zeta\left(s + \frac{2 \pi i}{\ln 2}x\right)</math> | ||
{{Todo|expand|inline=1|text=Make it clear how Fₛ(x) relates to the zeta function. Due to the sudden appearance of the natural logarithm and the imaginary unit i, this appears to have to do with complex exponentials, but it would be more approachable if the precise derivation was laid out here.}} | {{Todo|expand|inline=1|text=Make it clear how Fₛ(x) relates to the zeta function. Due to the sudden appearance of the natural logarithm and the imaginary unit i, this appears to have to do with complex exponentials (i.e. those found in the denominator of the terms of zeta when the input is complex), but it would be more approachable if the precise derivation was laid out here.}} | ||
If we take exponentials of both sides, then | If we take exponentials of both sides, then | ||