Riemann zeta function/Record lists: Difference between revisions

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{| class="wikitable center-all"
{| class="wikitable center-all"
!Record type
!Record type
![[1edo|1]]
![[1edt|1]]
![[2edo|2]]
![[2edt|2]]
![[3edo|3]]
![[4edt|4]]
![[5edo|5]]
![[9edt|9]]
![[7edo|7]]
![[13edt|13]]
![[10edo|10]]
![[17edt|17]]
![[12edo|12]]
![[26edt|26]]
![[19edo|19]]
![[39edt|39]]
![[31edo|31]]
![[88edt|88]]
![[41edo|41]]
![[114edt|114]]
![[53edo|53]]
![[131edt|131]]
![[130edo|130]]
![[800edt|800]]
![[171edo|171]]
![[914edt|914]]
![[270edo|270]]
![[1342edt|1342]]
![[494edo|494]]
![[1757edt|1757]]
![[1106edo|1106]]
![[2426edt|2426]]
![[1578edo|1578]]
![[3624edt|3624]]
![[2460edo|2460]]
![[3755edt|3755]]
![[2684edo|2684]]
!
![[3395edo|3395]]
!
![[5585edo|5585]]
!
![[6079edo|6079]]
!
![[8269edo|8269]]
!
![[8539edo|8539]]
!
|-
|-
|Zeta peak (cosine mu peak)
|Zeta peak (cosine mu peak)

Revision as of 22:19, 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 4 9 13 17 26 39 88 114 131 800 914 1342 1757 2426 3624 3755
Zeta peak (cosine mu peak) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Zeta integer (cosine mu integer) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
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