The Riemann zeta function and tuning: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 216384744 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 216384906 - 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 23: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-01 23:19:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>216384906</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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where E(q) is the error | where E(q) is the error | ||
[[math]] | [[math]] | ||
{b} | \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> | ||
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where E(q) is the error <br /> | where E(q) is the error <br /> | ||
<a class="wiki_link" href="/math">math</a> <br /> | <a class="wiki_link" href="/math">math</a> <br /> | ||
{b} | \frac{b}{N} - \log_2 q <br /> | ||
<a class="wiki_link" href="/math">math</a> <br /> | <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, 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 23:19, 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 23:19:43 UTC.
- The original revision id was 216384906.
- 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:3:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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:<h1> --><h1 id="toc0"><a name="Preliminaries"></a><!-- ws:end:WikiTextHeadingRule:1 -->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 />
<!-- 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 />
where E(q) is the error <br />
<a class="wiki_link" href="/math">math</a> <br />
\frac{b}{N} - \log_2 q <br />
<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, and the sum is over all primes up to p.</body></html>