The Riemann zeta function and tuning
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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>