The Riemann zeta function and tuning: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 217919276 - Original comment: ** |
Wikispaces>dguskin **Imported revision 217920262 - Original comment: ** |
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| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:dguskin|dguskin]] and made on <tt>2011-04-06 20:33:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>217920262</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=Preliminaries= | |||
=Preliminaries= | |||
Consider to start out with [[Tenney-Euclidean 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-Euclidean 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_2^p (\frac{E(q)}{\ln q})^2 | \sum_2^p (\frac{E(q)}{\ln q})^2 | ||
[[math]] | [[math]] | ||
where E(q) is the error | where E(q) is the error | ||
[[math]] | [[math]] | ||
\frac{b}{N} - \log_2 q | \frac{b}{N} - \log_2 q | ||
[[math]] | [[math]] | ||
of the [[patent val]] tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.</pre></div> | of the [[patent val]] tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.</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"><html><head><title>The Riemann Zeta Function and Tuning</title></head><body><!-- ws:start:WikiTextTocRule: | <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"><html><head><title>The Riemann Zeta Function and Tuning</title></head><body><!-- ws:start:WikiTextTocRule:4:&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:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Preliminaries">Preliminaries</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Preliminaries"></a><!-- ws:end:WikiTextHeadingRule:2 -->Preliminaries</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | Consider to start out with <a class="wiki_link" href="/Tenney-Euclidean%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 /> | ||
Consider to start out with <a class="wiki_link" href="/Tenney-Euclidean%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 /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextMathRule:0: | <!-- ws:start:WikiTextMathRule:0: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
\sum_2^p (\frac{E(q)}{\ln q})^2&lt;br/&gt;[[math]] | \sum_2^p (\frac{E(q)}{\ln q})^2&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\sum_2^p (\frac{E(q)}{\ln q})^2</script><!-- ws:end:WikiTextMathRule:0 --><br /> | --><script type="math/tex"> \sum_2^p (\frac{E(q)}{\ln q})^2</script><!-- ws:end:WikiTextMathRule:0 --> <br /> | ||
<br /> | <br /> | ||
where E(q) is the error <br /> | where E(q) is the error <br /> | ||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextMathRule:1: | ||
\frac{b}{N} - \log_2 q <br /> | [[math]]&lt;br/&gt; | ||
< | \frac{b}{N} - \log_2 q &lt;br/&gt;[[math]] | ||
--><script type="math/tex"> \frac{b}{N} - \log_2 q </script><!-- ws:end:WikiTextMathRule:1 --><br /> | |||
<br /> | <br /> | ||
of the <a class="wiki_link" href="/patent%20val">patent val</a> tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.</body></html></pre></div> | of the <a class="wiki_link" href="/patent%20val">patent val</a> tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.</body></html></pre></div> | ||
Revision as of 20:33, 6 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 dguskin and made on 2011-04-06 20:33:29 UTC.
- The original revision id was 217920262.
- 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-Euclidean 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_2^p (\frac{E(q)}{\ln q})^2
[[math]]
where E(q) is the error
[[math]]
\frac{b}{N} - \log_2 q
[[math]]
of the [[patent val]] tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.Original HTML content:
<html><head><title>The Riemann Zeta Function and Tuning</title></head><body><!-- ws:start:WikiTextTocRule:4:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Preliminaries">Preliminaries</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: -->
<!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc0"><a name="Preliminaries"></a><!-- ws:end:WikiTextHeadingRule:2 -->Preliminaries</h1>
Consider to start out with <a class="wiki_link" href="/Tenney-Euclidean%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 />
<br />
<!-- ws:start:WikiTextMathRule:0:
[[math]]<br/>
\sum_2^p (\frac{E(q)}{\ln q})^2<br/>[[math]]
--><script type="math/tex"> \sum_2^p (\frac{E(q)}{\ln q})^2</script><!-- ws:end:WikiTextMathRule:0 --> <br />
<br />
where E(q) is the error <br />
<br />
<!-- ws:start:WikiTextMathRule:1:
[[math]]<br/>
\frac{b}{N} - \log_2 q <br/>[[math]]
--><script type="math/tex"> \frac{b}{N} - \log_2 q </script><!-- ws:end:WikiTextMathRule:1 --><br />
<br />
of the <a class="wiki_link" href="/patent%20val">patent val</a> tuning, meaning the nearest to q, of the prime q, and the sum is over all primes up to p.</body></html>