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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12133 |
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| _version_ | 1866914261288091648 |
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| author | Śliwiński, Dominik |
| author_facet | Śliwiński, Dominik |
| contents | This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(λ, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $ζ\left(\frac{1}{2} +is\right)$ as $λ, N \rightarrow \infty$. It turns out that when considering different standard notions of error, the dissonance between the spectra and Riemann $ζ$ zeros either appears to or can be proven to be inverse logarithmic in nature, which elegantly fits the distribution of prime numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Analysis of the $D_{\log}^{(λ, N)}$ Operators Śliwiński, Dominik Spectral Theory Number Theory 47N99 (Primary) 46N99, 11M06 (Secondary) This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(λ, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $ζ\left(\frac{1}{2} +is\right)$ as $λ, N \rightarrow \infty$. It turns out that when considering different standard notions of error, the dissonance between the spectra and Riemann $ζ$ zeros either appears to or can be proven to be inverse logarithmic in nature, which elegantly fits the distribution of prime numbers. |
| title | Spectral Analysis of the $D_{\log}^{(λ, N)}$ Operators |
| topic | Spectral Theory Number Theory 47N99 (Primary) 46N99, 11M06 (Secondary) |
| url | https://arxiv.org/abs/2601.12133 |