Riemann zeta function/Record lists: Difference between revisions

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added sigma = 2 peaks
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{| class="wikitable"
{| class="wikitable"
!Record type
!Record type
!1
![[1edo|1]]
!2
![[2edo|2]]
!3
![[3edo|3]]
!5
![[5edo|5]]
!7
![[7edo|7]]
!12
![[12edo|12]]
!19
![[19edo|19]]
!31
![[31edo|31]]
!41
![[41edo|41]]
!53
![[53edo|53]]
!130
![[130edo|130]]
!171
![[171edo|171]]
!270
![[270edo|270]]
!1578
![[1578edo|1578]]
!2460
![[2460edo|2460]]
!2684
![[2684edo|2684]]
!3395
![[3395edo|3395]]
!6079
![[6079edo|6079]]
!8269
![[8269edo|8269]]
!
!
!
!
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|Absolute zeta peak
|Absolute zeta peak
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|Real zeta peak (cosine mu peak)
|Real zeta peak (cosine mu peak)
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Revision as of 15:20, 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 = 0.5

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 = 2

Record type 1 2 3 5 7 12 19 31 41 53 130 171 270 1578 2460 2684 3395 6079 8269
Absolute zeta peak ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Absolute zeta integer
Real zeta peak (cosine mu peak) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Real zeta integer (cosine mu integer)
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