Riemann zeta function/Record lists: Difference between revisions

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Lériendil (talk | contribs)
8,046 edits
added 3/2 section, filled it with 2 values fn
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== σ = 3/2 ==
{| class="wikitable"
!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]]
|-
|Absolute zeta peak
| ★
| ★
| ★
| ★
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| ★
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| ★
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|Absolute zeta integer
| ★
| ★
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| ★
| ★
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| ★
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| ★
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|Real zeta peak (cosine mu peak)
| ★
| ★
| ★
| ★
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| ★
| ★
| ★
| ★
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| ★
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| ★
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|-
|Real zeta integer (cosine mu integer)
| ★
| ★
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| ★
| ★
| ★
| ★
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| ★
| ★
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Revision as of 15:38, 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 = 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 = 3/2

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
Absolute zeta peak ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Absolute zeta integer ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Real zeta peak (cosine mu peak) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Real zeta integer (cosine mu integer) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★

σ = 2

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
Absolute zeta peak ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Absolute zeta integer ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Real zeta peak (cosine mu peak) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
Real zeta integer (cosine mu integer) ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
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