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

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Zenodo2026-03-28 更新2026-05-29 收录
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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 γ The 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 zero Key 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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Zenodo
创建时间:
2026-03-28
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