Riemann zeta function/Record lists: Difference between revisions
Jump to navigation
Jump to search
consolidated |
No edit summary |
||
| Line 489: | Line 489: | ||
For σ = 2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo. | For σ = 2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo. | ||
{| class="wikitable center-all" | |||
!Record type | |||
![[1edo|1]] | |||
![[2edo|2]] | |||
![[3edo|3]] | |||
![[5edo|5]] | |||
![[7edo|7]] | |||
![[10edo|10]] | |||
![[12edo|12]] | |||
![[19edo|19]] | |||
![[31edo|31]] | |||
![[41edo|41]] | |||
![[53edo|53]] | |||
![[130edo|130]] | |||
![[171edo|171]] | |||
![[270edo|270]] | |||
![[494edo|494]] | |||
![[1106edo|1106]] | |||
![[1578edo|1578]] | |||
![[2460edo|2460]] | |||
![[2684edo|2684]] | |||
![[3395edo|3395]] | |||
![[5585edo|5585]] | |||
![[6079edo|6079]] | |||
![[8269edo|8269]] | |||
![[8539edo|8539]] | |||
|- | |||
|Zeta peak (cosine mu peak) | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| | |||
|- | |||
|Zeta integer (cosine mu integer) | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| ★ | |||
| | |||
| ★ | |||
| | |||
| | |||
| ★ | |||
| | |||
| | |||
| ★ | |||
|} | |||
=== No-twos tritave divisions === | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
!Record type | !Record type | ||
Revision as of 22:15, 10 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
For σ = 3/2, 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 | 72 | 130 | 171 | 224 | 270 | 494 | 1106 | 1578 | 2460 | 2684 | 3395 | 5585 | 8269 | 8539 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zeta peak | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zeta peak (cosine mu peak) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| Zeta integer (cosine mu integer) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |
No-twos tritave divisions
| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Zeta peak (cosine mu peak) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | |||||
| Zeta integer (cosine mu integer) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |