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.
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| Zeta integral
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| Zeta gap
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σ = 0.5
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| Absolute zeta peak
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| Absolute zeta integer
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| Real zeta peak
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| Real zeta integer
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σ = 1
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| Absolute zeta peak
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| Absolute zeta integer
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| Real zeta peak
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| Real zeta integer
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σ = 3/2
| Record type
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1
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2
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3
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5
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7
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10
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12
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19
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31
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41
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53
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72
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130
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171
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224
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270
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494
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1106
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1578
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2460
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2684
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3395
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5585
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8269
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8539
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| Absolute zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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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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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Real zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Real zeta integer
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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σ = 2
| Record type
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1
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2
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3
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5
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7
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10
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12
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19
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31
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41
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53
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130
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171
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270
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494
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1106
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1578
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2460
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2684
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3395
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5585
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6079
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8269
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8539
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| Absolute zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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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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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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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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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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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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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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