Ryan's Working Page: Difference between revisions

BudjarnLambeth (talk | contribs)
m Add outgoing links to dead end page
ArrowHead294 (talk | contribs)
mNo edit summary
 
Line 6: Line 6:
\left| \zeta(s) \right|^2 = \zeta(2a) + 2 \sum_{n > d} \left[\frac{\cos\left(b\ln\left(\tfrac{n}{d}\right)\right)}{(nd)^{a}}\right]</math>
\left| \zeta(s) \right|^2 = \zeta(2a) + 2 \sum_{n > d} \left[\frac{\cos\left(b\ln\left(\tfrac{n}{d}\right)\right)}{(nd)^{a}}\right]</math>


The cosines are weighted by 1/(nd)<span style="font-size: 11.6999998092651px; vertical-align: super;">a</span>. However, it is of interest to replace n*d with max(n,d)^2 to see if we can derive a [[Weil norm, Tenney-Weil norm, and TWp interval and tuning space|Weil]]-weighted analog of the Zeta function. I will denote this function by f(s).
The cosines are weighted by 1/(nd)<span style="font-size: 11.6999998092651px; vertical-align: super;">a</span>. However, it is of interest to replace n*d with max(n,d)^2 to see if we can derive a [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space|Weil]]-weighted analog of the Zeta function. I will denote this function by f(s).


<math>\displaystyle
<math>\displaystyle