The Riemann zeta function and tuning: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 216383068 - Original comment: **
 
Wikispaces>genewardsmith
**Imported revision 216383156 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2011-04-01 22:58:59 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-01 23:00:06 UTC</tt>.<br>
: The original revision id was <tt>216383068</tt>.<br>
: The original revision id was <tt>216383156</tt>.<br>
: The revision comment was: <tt></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>
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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Consider to start out with [[Tenney-Eucliedan metrics|Tenney-Euclidean error]]. For some [[equal]] division N in the [[p-limit]], this can be defined as the square root of the quantity
Consider to start out with [[Tenney-Eucliedan metrics|Tenney-Euclidean error]]. For some [[equal]] division N in the [[p-limit]], this can be defined as the square root of the quantity
[[math]]
[[math]]
\sum_{q prime &lt;= p} (\frac{E(q){\ln q})^2
\sum_{q prime \le p} (\frac{E(q){\ln q})^2
[[math]]
[[math]]
where E(q) is the error [[math]] \frac{b}{N} - \lb(q) [[math]] of the [[patent val]] tuning, meaning the nearest to q, of the prime q.</pre></div>
where E(q) is the error  
[[math]] \frac{b}{N} - \lb q [[math]]  
of the [[patent val]] tuning, meaning the nearest to q, of the prime q.</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Riemann Zeta Function and Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:3:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:3 --&gt;&lt;!-- ws:start:WikiTextTocRule:4: --&gt;&lt;a href="#Preliminaries"&gt;Preliminaries&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Riemann Zeta Function and Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:3:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:3 --&gt;&lt;!-- ws:start:WikiTextTocRule:4: --&gt;&lt;a href="#Preliminaries"&gt;Preliminaries&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;
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&lt;!-- ws:start:WikiTextMathRule:0:
&lt;!-- ws:start:WikiTextMathRule:0:
[[math]]&amp;lt;br/&amp;gt;
[[math]]&amp;lt;br/&amp;gt;
\sum_{q prime &amp;lt;= p} (\frac{E(q){\ln q})^2&amp;lt;br/&amp;gt;[[math]]
\sum_{q prime \le p} (\frac{E(q){\ln q})^2&amp;lt;br/&amp;gt;[[math]]
  --&gt;&lt;script type="math/tex"&gt;\sum_{q prime &lt;= p} (\frac{E(q){\ln q})^2&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
  --&gt;&lt;script type="math/tex"&gt;\sum_{q prime \le p} (\frac{E(q){\ln q})^2&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
where E(q) is the error &lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt; \frac{b}{N} - \lb(q) &lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt; of the &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; tuning, meaning the nearest to q, of the prime q.&lt;/body&gt;&lt;/html&gt;</pre></div>
where E(q) is the error &lt;br /&gt;
&lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt; \frac{b}{N} - \lb q &lt;a class="wiki_link" href="/math"&gt;math&lt;/a&gt; &lt;br /&gt;
of the &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; tuning, meaning the nearest to q, of the prime q.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 23:00, 1 April 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2011-04-01 23:00:06 UTC.
The original revision id was 216383156.
The revision comment was:

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

Original Wikitext content:

[[toc|flat]]

=Preliminaries=
Consider to start out with [[Tenney-Eucliedan metrics|Tenney-Euclidean error]]. For some [[equal]] division N in the [[p-limit]], this can be defined as the square root of the quantity
[[math]]
\sum_{q prime \le p} (\frac{E(q){\ln q})^2
[[math]]
where E(q) is the error 
[[math]] \frac{b}{N} - \lb q [[math]] 
of the [[patent val]] tuning, meaning the nearest to q, of the prime q.

Original HTML content:

<html><head><title>The Riemann Zeta Function and Tuning</title></head><body><!-- ws:start:WikiTextTocRule:3:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:3 --><!-- ws:start:WikiTextTocRule:4: --><a href="#Preliminaries">Preliminaries</a><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: -->
<!-- ws:end:WikiTextTocRule:5 --><br />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Preliminaries"></a><!-- ws:end:WikiTextHeadingRule:1 -->Preliminaries</h1>
Consider to start out with <a class="wiki_link" href="/Tenney-Eucliedan%20metrics">Tenney-Euclidean error</a>. For some <a class="wiki_link" href="/equal">equal</a> division N in the <a class="wiki_link" href="/p-limit">p-limit</a>, this can be defined as the square root of the quantity<br />
<!-- ws:start:WikiTextMathRule:0:
[[math]]&lt;br/&gt;
\sum_{q prime \le p} (\frac{E(q){\ln q})^2&lt;br/&gt;[[math]]
 --><script type="math/tex">\sum_{q prime \le p} (\frac{E(q){\ln q})^2</script><!-- ws:end:WikiTextMathRule:0 --><br />
where E(q) is the error <br />
<a class="wiki_link" href="/math">math</a> \frac{b}{N} - \lb q <a class="wiki_link" href="/math">math</a> <br />
of the <a class="wiki_link" href="/patent%20val">patent val</a> tuning, meaning the nearest to q, of the prime q.</body></html>
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