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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17802494 |
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| _version_ | 1866901387795759104 |
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| author | YILMAZ, AYDIN |
| author_facet | YILMAZ, AYDIN |
| contents | <p>Using only publicly available data from Odlyzko’s tables, we present two mutually independent, ultra-minimal models that predict the imaginary parts of the first 10⁸ nontrivial zeros of the Riemann zeta function with remarkable accuracy:</p> <p> </p> <p>1. A fixed-weight hybrid extrapolation calibrated solely on the first 11 zeros maintains absolute errors below 1 800 units up to n = 10⁸ — a 177-fold improvement over the classical Riemann–von Mangoldt asymptotic alone.</p> <p> </p> <p>2. A three-parameter stochastic feedback process γ_k = ϕ γ_{k−1} + δ log(2π(k + 10)) + ε_k fitted by OLS to the first 1000 zeros yields ϕ ≈ 0.8714 < 1 with R² = 0.9999997 and parameters stable across eight orders of magnitude.</p> <p> </p> <p>Both models exhibit extreme fragility to even tiny systematic deviations from the critical line, yet no such deviation is observed. These findings provide compelling numerical evidence supporting the Riemann Hypothesis up to height ≈ 2.2 × 10¹⁰. Both models remain stable across eight orders of magnitude despite their extreme structural simplicity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17802494 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Two Independent Ultra-Minimal Predictive Models for the First 10⁸ Nontrivial Zeros of the Riemann Zeta Function YILMAZ, AYDIN <p>Using only publicly available data from Odlyzko’s tables, we present two mutually independent, ultra-minimal models that predict the imaginary parts of the first 10⁸ nontrivial zeros of the Riemann zeta function with remarkable accuracy:</p> <p> </p> <p>1. A fixed-weight hybrid extrapolation calibrated solely on the first 11 zeros maintains absolute errors below 1 800 units up to n = 10⁸ — a 177-fold improvement over the classical Riemann–von Mangoldt asymptotic alone.</p> <p> </p> <p>2. A three-parameter stochastic feedback process γ_k = ϕ γ_{k−1} + δ log(2π(k + 10)) + ε_k fitted by OLS to the first 1000 zeros yields ϕ ≈ 0.8714 < 1 with R² = 0.9999997 and parameters stable across eight orders of magnitude.</p> <p> </p> <p>Both models exhibit extreme fragility to even tiny systematic deviations from the critical line, yet no such deviation is observed. These findings provide compelling numerical evidence supporting the Riemann Hypothesis up to height ≈ 2.2 × 10¹⁰. Both models remain stable across eight orders of magnitude despite their extreme structural simplicity.</p> |
| title | Two Independent Ultra-Minimal Predictive Models for the First 10⁸ Nontrivial Zeros of the Riemann Zeta Function |
| url | https://doi.org/10.5281/zenodo.17802494 |