Version 1.0

Zeta Prime Dataset: |ζ'(½+iy)| at Zeros of the Riemann Zeta Function via T8/T9

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Tikhonov, Alexei

Description

This dataset contains |Z'(γ)| = |ζ'(½+iγ)| for 6,582 non-trivial zeros of the Riemann zeta function, computed via the exact T9 identity:|ζ'(½+iγ)| = |Z'(γ)| at every zero γThe data spans t ∈ [100, 10100] with:- γ: zero location- Zp_abs: |Z'(γ)| (the "strength" of the zero)- log_Zp: log|Z'(γ)|- mean_sp: local mean spacing 2π/log(γ/2π)- delta_prev_norm: normalized spacing to previous zeroKey findings (included in the dataset):- |Z'(γ)| ~ LogNormal(μ=0.748, σ=0.310)- Strong zeros are 20% closer to neighbors (p = 0.035)- Spearman correlation ρ(|Z'|, s_sym) = 0.72 (p < 10⁻⁸)This is the first public dataset of |ζ'(½+iγ)| at zeros.For T8 continuous data (|ζ'(½+it)|² for 10,000 points), see dataset_T8_continuous.csv.Formats: CSV, ready for analysis in Python/R/Matlab.Related:- T8: |ζ'(½+it)|² = (θ'Z)² + (Z')²- T9: |ζ'(½+iγ)| = |Z'(γ)|- Paper: arXiv:XXXX.XXXXX (forthcoming)License: CC BY 4.0 for academic use. Commercial licensing: contact via GitHub.

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Metrics

Dataset Index

0.4

FAIR Score

85%

Citations

0

Mentions

0

Metrics Over Time

Publication Details

DOI

Publisher

Zenodo

License

Creative Commons Attribution 4.0 International

Assigned Domain

Subfield

Mathematical Physics

Field

Mathematics

Domain

Physical Sciences

Confidence Score

39%

Source

Scholar Data Model

Keywords

Reimann zeta function,Hardy functionzeta derivativeT9 theoremRandom matrix theoryZerosL-functionsNumerical analysis

Normalization Factors

FT

73.08

CTw

1.00

MTw

1.00