The Riemann zeta function and tuning: Difference between revisions

ArrowHead294 (talk | contribs)
Sintel (talk | contribs)
Removing primes: fix missing minus sign
Line 680: Line 680:
Along the critical line:
Along the critical line:


<math>
<math>\displaystyle{
\displaystyle\abs{1 - p^{\frac{1}{2} - it}} = \sqrt{1 + \frac{1}{p} - \frac{2 \cos(t \ln p)}{\sqrt{p}}}
\left| 1 - p^{-\frac{1}{2} - it} \right| = \sqrt{1 + \frac{1}{p} - \frac{2 \cos(t \ln p)}{\sqrt{p}}}
</math>
}</math>


Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime ''p'' removed from consideration. Zeta peak and zeta integral tunings may then be found as before.
Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime ''p'' removed from consideration. Zeta peak and zeta integral tunings may then be found as before.