Wilson norm: Difference between revisions
No edit summary |
No edit summary |
||
| Line 5: | Line 5: | ||
Note that we have <math>\text{sopfr}(pq) = \text{sopfr}(p) + \text{sopfr}(q)</math>, similar to the logarithm -- as a result, this function is sometimes even referred to as the "integer logarithm." So, equivalently, we can define the Wilson height of a rational number p/q as the Wilson height of p, plus the Wilson height of q. | Note that we have <math>\text{sopfr}(pq) = \text{sopfr}(p) + \text{sopfr}(q)</math>, similar to the logarithm -- as a result, this function is sometimes even referred to as the "integer logarithm." So, equivalently, we can define the Wilson height of a rational number p/q as the Wilson height of p, plus the Wilson height of q. | ||
One important theorem is that the Wilson-optimal tuning happens to also be the Benedetti optimal tuning for subgroups with a pairwise coprime basis (e.g. prime limits and some others); see also [[BOP | One important theorem is that the Wilson-optimal tuning happens to also be the Benedetti optimal tuning for subgroups with a pairwise coprime basis (e.g. prime limits and some others); see also [[BOP Tuning]]. | ||
== Example == | == Example == | ||