| _version_ | 1866901528854396928 |
|---|---|
| author | Tripi, Thomas |
| author_facet | Tripi, Thomas |
| contents | <p>The nontrivial zeros of the Riemann zeta function are described through density and spacing.<br>Computations on the first one hundred zeros reveal five regimes in the response of curvature as<br>the measurement scale changes, from pole behavior to bulk density. Perturbations produce a<br>response that follows a common normalized curve across dyadic bands. A rank relation between<br>normalized curvature and local inverse spacing appears, with Spearman correlation near −0.841<br>for the true zeros. Systems constructed to match the gap distribution produce correlations near<br>zero, with separation approximately 0.838. Gap distribution determines magnitude. Ordering<br>defines arrangement. A bandwise response analysis shows that peak location remains fixed<br>at σ = 1/2 across all scales, while peak sharpness varies with measurement window: location<br>invariant, structure scale-dependent.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19601010 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Ordering and Deformation in the Zeros of the Riemann Zeta Function Tripi, Thomas Riemann Zeta Function nontrivial zeros spacing statistics curvature analysis surrogate test ordering structure empirical number theory <p>The nontrivial zeros of the Riemann zeta function are described through density and spacing.<br>Computations on the first one hundred zeros reveal five regimes in the response of curvature as<br>the measurement scale changes, from pole behavior to bulk density. Perturbations produce a<br>response that follows a common normalized curve across dyadic bands. A rank relation between<br>normalized curvature and local inverse spacing appears, with Spearman correlation near −0.841<br>for the true zeros. Systems constructed to match the gap distribution produce correlations near<br>zero, with separation approximately 0.838. Gap distribution determines magnitude. Ordering<br>defines arrangement. A bandwise response analysis shows that peak location remains fixed<br>at σ = 1/2 across all scales, while peak sharpness varies with measurement window: location<br>invariant, structure scale-dependent.</p> |
| title | Ordering and Deformation in the Zeros of the Riemann Zeta Function |
| topic | Riemann Zeta Function nontrivial zeros spacing statistics curvature analysis surrogate test ordering structure empirical number theory |
| url | https://doi.org/10.5281/zenodo.19601010 |