Wilson norm: Difference between revisions
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[[File:WilsonHeightIntegerLimit.png|200px|thumb|right|Diagram by Lériendil showing the Wilson height (vertical axis) versus integer limit (horizontal axis) of simple intervals.]] The '''Wilson height''' is a different way of weighting rational numbers than the [[Tenney height]], but has some very beneficial properties that make it an excellent metric to look at. | [[File:WilsonHeightIntegerLimit.png|200px|thumb|right|Diagram by Lériendil showing the Wilson height (vertical axis) versus integer limit (horizontal axis) of simple intervals.]]The '''Wilson height''' is a different way of weighting rational numbers than the [[Tenney height]], but has some very beneficial properties that make it an excellent metric to look at. | ||
If p/q is a positive rational number reduced to its lowest terms, then the Wilson height is the [http://mathworld.wolfram.com/SumofPrimeFactors.html "sum of prime factors with repetition"] of the number p*q, counting multiplicity. This function is often written <math>\text{sopfr}(pq)</math>. | If p/q is a positive rational number reduced to its lowest terms, then the Wilson height is the [http://mathworld.wolfram.com/SumofPrimeFactors.html "sum of prime factors with repetition"] of the number p*q, counting multiplicity. This function is often written <math>\text{sopfr}(pq)</math>. | ||