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2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.17658230 |
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| _version_ | 1866901160047149056 |
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| author | Kawasaki, Hideyo |
| author_facet | Kawasaki, Hideyo |
| contents | <p>We establish a duality between (i) normality of real-number expansions and (ii) GUE-type<br>zero spacing for automorphic L–functions, arising naturally from the Mellin-free Fredholm<br>framework of CMTMB I–V. The key observation is that both phenomena are governed<br>by the same Gaussian Fredholm deformation: finite–κ kernels enforce positive spacing and<br>uniform digit frequencies, while the limit κ → 0+ transmits these structural constraints<br>to the automorphic and arithmetic spectra. This provides a unified explanation of the<br>Montgomery–Dyson law and Borel’s normality conjecture.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17658230 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Conservative Motion Theory – MB VI: Normality–Spacing Duality under Mellin–Free Fredholm Kernels Kawasaki, Hideyo <p>We establish a duality between (i) normality of real-number expansions and (ii) GUE-type<br>zero spacing for automorphic L–functions, arising naturally from the Mellin-free Fredholm<br>framework of CMTMB I–V. The key observation is that both phenomena are governed<br>by the same Gaussian Fredholm deformation: finite–κ kernels enforce positive spacing and<br>uniform digit frequencies, while the limit κ → 0+ transmits these structural constraints<br>to the automorphic and arithmetic spectra. This provides a unified explanation of the<br>Montgomery–Dyson law and Borel’s normality conjecture.</p> |
| title | Conservative Motion Theory – MB VI: Normality–Spacing Duality under Mellin–Free Fredholm Kernels |
| url | https://doi.org/10.5281/zenodo.17658230 |