The Riemann zeta function and tuning: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 13:34:09 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 13:36:14 UTC</tt>.<br>

: The original revision id was <tt>~~250508176~~</tt>.<br>

: The original revision id was <tt>250508378</tt>.<br>

: The revision comment was: <tt></tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

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[[math]]

1 + \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}

1 + \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}

[[math]]

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<!-- ws:start:WikiTextMathRule:12:

[[math]]&lt;br/&gt;

1 + \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}&lt;br/&gt;[[math]]

1 + \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}&lt;br/&gt;[[math]]

--><script type="math/tex">1 + \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}</script><br />

--><script type="math/tex">1 + \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}</script><br />

<br />

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.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 13:34:09 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 13:36:14 UTC</tt>.<br>
-: The original revision id was <tt>250508176</tt>.<br>
+: The original revision id was <tt>250508378</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 127: / Line 127: @@
 [[math]]
-+ \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}
++ \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}
 [[math]]
@@ Line 284: / Line 284: @@
 &lt;!-- ws:start:WikiTextMathRule:12:
 [[math]]&amp;lt;br/&amp;gt;
-+ \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}&amp;lt;br/&amp;gt;[[math]]
++ \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}&amp;lt;br/&amp;gt;[[math]]
-  --&gt;&lt;script type="math/tex"&gt;1 + \frac{1}{p} - \frac{2 \cos(\ln\ p t)}{\sqrt{p}}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:12 --&gt;&lt;br /&gt;
+  --&gt;&lt;script type="math/tex"&gt;1 + \frac{1}{p} - \frac{2 \cos(\ln p\ t)}{\sqrt{p}}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:12 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 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.&lt;br /&gt;