| _version_ | 1866901906136236032 |
|---|---|
| author | Michalski, Michał |
| author_facet | Michalski, Michał |
| contents | <p>We present the discovery of a deterministic multi-fractal structure based on the golden ratio φ, which organizes the distribution of Riemann zeta function zeros and prime numbers. Analyzing the spectral repulsion coefficient β for samples from 10^2 to 10^8 zeros, we observed a systematic increase in values from β=3.894 to β=11.778. This phenomenon, initially interpreted as a numerical anomaly, turned out to be a manifestation of a hierarchical structure in which 61.803...% of elements remain at a given fractal level (exactly 1/φ), while 38.196...% proceed to deeper levels (exactly 1 - 1/φ). Verification conducted on three independent datasets: (i) 100,000,000 zeta function zeros with 31 significant digits precision, (ii) 20,000 zeros with 745 significant digits precision, and (iii) 5,761,455 prime numbers up to 10^8, confirms the universality of the structure.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16875033 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Universal Multi-fractal Structure φ in the Distribution of Zeta Function Zeros and Prime Numbers Michalski, Michał <p>We present the discovery of a deterministic multi-fractal structure based on the golden ratio φ, which organizes the distribution of Riemann zeta function zeros and prime numbers. Analyzing the spectral repulsion coefficient β for samples from 10^2 to 10^8 zeros, we observed a systematic increase in values from β=3.894 to β=11.778. This phenomenon, initially interpreted as a numerical anomaly, turned out to be a manifestation of a hierarchical structure in which 61.803...% of elements remain at a given fractal level (exactly 1/φ), while 38.196...% proceed to deeper levels (exactly 1 - 1/φ). Verification conducted on three independent datasets: (i) 100,000,000 zeta function zeros with 31 significant digits precision, (ii) 20,000 zeros with 745 significant digits precision, and (iii) 5,761,455 prime numbers up to 10^8, confirms the universality of the structure.</p> |
| title | Universal Multi-fractal Structure φ in the Distribution of Zeta Function Zeros and Prime Numbers |
| url | https://doi.org/10.5281/zenodo.16875033 |