The Riemann zeta function and tuning: Difference between revisions
Wikispaces>genewardsmith **Imported revision 556855999 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 573457423 - 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> | ||
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Now suppose that ||x|| denotes the difference between x and the integer nearest to x. For example, ||8.202|| would be .202, since it's the difference between 8.202 and the nearest integer, which is 8. ||7.95|| would be .05, which is the difference between 7.95 and the nearest integer, which is 8. Mathematically speaking, ||x|| denotes the function x - floor(x+1/2). | Now suppose that ||x|| denotes the difference between x and the integer nearest to x. For example, ||8.202|| would be .202, since it's the difference between 8.202 and the nearest integer, which is 8. ||7.95|| would be .05, which is the difference between 7.95 and the nearest integer, which is 8. Mathematically speaking, ||x|| denotes the function x - floor(x+1/2). | ||
For any value of x, we can construct a p-limit [[patent val]]. We do so by rounding log2(q)*x to the nearest integer for each prime q up to p. The [[Tenney-Euclidean metrics|Tenney-Euclidean error]] for this val will be | For any value of x, we can construct a p-limit [[patent val]]. We do so by rounding log2(q)*x to the nearest integer for each prime q up to p. The [[Tenney-Euclidean metrics|the square of the Tenney-Euclidean error]] for this val will be | ||
[[math]] | [[math]] | ||
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Now suppose that ||x|| denotes the difference between x and the integer nearest to x. For example, ||8.202|| would be .202, since it's the difference between 8.202 and the nearest integer, which is 8. ||7.95|| would be .05, which is the difference between 7.95 and the nearest integer, which is 8. Mathematically speaking, ||x|| denotes the function x - floor(x+1/2).<br /> | Now suppose that ||x|| denotes the difference between x and the integer nearest to x. For example, ||8.202|| would be .202, since it's the difference between 8.202 and the nearest integer, which is 8. ||7.95|| would be .05, which is the difference between 7.95 and the nearest integer, which is 8. Mathematically speaking, ||x|| denotes the function x - floor(x+1/2).<br /> | ||
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For any value of x, we can construct a p-limit <a class="wiki_link" href="/patent%20val">patent val</a>. We do so by rounding log2(q)*x to the nearest integer for each prime q up to p. The <a class="wiki_link" href="/Tenney-Euclidean%20metrics">Tenney-Euclidean error</a> for this val will be<br /> | For any value of x, we can construct a p-limit <a class="wiki_link" href="/patent%20val">patent val</a>. We do so by rounding log2(q)*x to the nearest integer for each prime q up to p. The <a class="wiki_link" href="/Tenney-Euclidean%20metrics">the square of the Tenney-Euclidean error</a> for this val will be<br /> | ||
<br /> | <br /> | ||
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