The Riemann zeta function and tuning: Difference between revisions
Wikispaces>genewardsmith **Imported revision 217978538 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 217978814 - 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>2011-04-07 00: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-07 00:58:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>217978814</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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[[math]] | [[math]] | ||
This now increases to a maximum value for low-errors, rather than declining to a minimum. Of more interest is the fact that it is a known mathematical function, which can be expressed in terms of the [[http://en.wikipedia.org/wiki/Riemann_zeta_function|Riemann zeta function: | This now increases to a maximum value for low-errors, rather than declining to a minimum. Of more interest is the fact that it is a known mathematical function, which can be expressed in terms of the real part of the logarithm of the [[http://en.wikipedia.org/wiki/Riemann_zeta_function|Riemann zeta function]]: | ||
[[math]] | [[math]] | ||
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--><script type="math/tex">F_s(x) = \sum_1^\infty \frac{\Lambda(n)}{\ln n} \frac{\cos(2 \pi x)}{n^s}</script><!-- ws:end:WikiTextMathRule:4 --><br /> | --><script type="math/tex">F_s(x) = \sum_1^\infty \frac{\Lambda(n)}{\ln n} \frac{\cos(2 \pi x)}{n^s}</script><!-- ws:end:WikiTextMathRule:4 --><br /> | ||
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This now increases to a maximum value for low-errors, rather than declining to a minimum. Of more interest is the fact that it is a known mathematical function, which can be expressed in terms of the | This now increases to a maximum value for low-errors, rather than declining to a minimum. Of more interest is the fact that it is a known mathematical function, which can be expressed in terms of the real part of the logarithm of the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Riemann_zeta_function" rel="nofollow">Riemann zeta function</a>:<br /> | ||
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