Riemann zeta function/Record lists: Difference between revisions
Jump to navigation
Jump to search
was misinformed about my calcs; am recalculating |
reädded the absolute |
||
| Line 401: | Line 401: | ||
== σ = 3/2 == | == σ = 3/2 == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
!Record type | !Record type | ||
| Line 430: | Line 428: | ||
![[8269edo|8269]] | ![[8269edo|8269]] | ||
![[8539edo|8539]] | ![[8539edo|8539]] | ||
|- | |||
|Absolute zeta peak | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| | |||
| | |||
| ★ | |||
| ★ | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|Absolute zeta integer | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| | |||
| ★ | |||
| | |||
| ★ | |||
|- | |- | ||
|Real zeta peak | |Real zeta peak | ||
Revision as of 19:11, 11 April 2025
Zero-based metrics
Zeta metrics corresponding to regions between zeros on the critical line (σ = 0.5). The Riemann hypothesis is the equivalent to the statement that these correspond directly to peaks.
| Record type | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zeta integral | ||||||||||||||||||||||||||||
| Zeta gap |
σ = 1/2
| Record type | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Absolute zeta peak | ||||||||||||||||||||||||||||
| Absolute zeta integer | ||||||||||||||||||||||||||||
| Real zeta peak | ||||||||||||||||||||||||||||
| Real zeta integer |
σ = 1
| Record type | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Absolute zeta peak | ||||||||||||||||||||||||||||
| Absolute zeta integer | ||||||||||||||||||||||||||||
| Real zeta peak | ||||||||||||||||||||||||||||
| Real zeta integer |
σ = 3/2
| Record type | 1 | 2 | 3 | 5 | 7 | 10 | 12 | 19 | 31 | 41 | 53 | 72 | 130 | 171 | 224 | 270 | 494 | 1106 | 1578 | 2460 | 2684 | 3395 | 5585 | 8269 | 8539 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Absolute zeta peak | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||||||
| Absolute zeta integer | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| Real zeta peak | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| Real zeta integer | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |
No-twos tritave divisions
| Record type | 1 | 2 | 4 | 9 | 13 | 17 | 26 | 39 | 88 | 114 | 131 | 415 | 712 | 800 | 914 | 1342 | 1757 | 2426 | 3624 | 3755 | 6181 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Real zeta peak | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ||
| Real zeta integer | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |
σ = 2
For σ = 2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo.
| Record type | 1 | 2 | 3 | 5 | 7 | 10 | 12 | 19 | 31 | 41 | 53 | 130 | 171 | 270 | 494 | 1106 | 1578 | 2460 | 2684 | 3395 | 5585 | 6079 | 8269 | 8539 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Real zeta peak (cosine mu peak) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| Real zeta integer (cosine mu integer) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |
No-twos tritave divisions
| Record type | 1 | 2 | 4 | 9 | 13 | 17 | 26 | 39 | 88 | 114 | 131 | 800 | 914 | 1342 | 1757 | 2426 | 3624 | 3755 | 6181 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Real zeta peak (cosine mu peak) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |
| Real zeta integer (cosine mu integer) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |