Riemann zeta function/Record lists: Difference between revisions
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== σ = 3/2 == | == σ = 3/2 == | ||
For σ = 3/2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo. | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
!Record type | !Record type | ||
| Line 429: | Line 431: | ||
![[8539edo|8539]] | ![[8539edo|8539]] | ||
|- | |- | ||
| | |Zeta peak | ||
| ★ | | ★ | ||
| ★ | | ★ | ||
| Line 510: | Line 458: | ||
| ★ | | ★ | ||
|- | |- | ||
| | |Zeta integer | ||
| ★ | | ★ | ||
| ★ | | ★ | ||
| Line 539: | Line 487: | ||
== σ = 2 == | == σ = 2 == | ||
For σ = 2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo. | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
!Record type | !Record type | ||
| Line 566: | Line 516: | ||
![[8539edo|8539]] | ![[8539edo|8539]] | ||
|- | |- | ||
| | |Zeta peak (cosine mu peak) | ||
| ★ | | ★ | ||
| ★ | | ★ | ||
| Line 589: | Line 539: | ||
| | | | ||
| ★ | | ★ | ||
| ★ | | ★ | ||
| | | | ||
|- | |- | ||
| | |Zeta integer (cosine mu integer) | ||
| ★ | | ★ | ||
| ★ | | ★ | ||
Revision as of 21:38, 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) | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ | ★ |