Riemann zeta function/Record lists: Difference between revisions

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Revision as of 16:05, 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 72 130 171 224 270 494 1106 1578 2460 2684 3395 5585 8269 8539
Absolute zeta peak ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ s ★ ★ t ★ ★ ★ ★ ★ ★ ★
Absolute zeta integer ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ s ★ ★ t ★ ★ ★ ★ ★ ★
Real zeta peak ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ s ★ ★ t ★ ★ ★ ★ ★ ★ ★
Real zeta integer ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ s ★ ★ t ★ ★ ★ ★ ★ ★

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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