Diffraction of the primes and other sets of zero density
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914028150849536 |
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| author | Humeniuk, Adam Ramsey, Christopher Strungaru, Nicolae |
| author_facet | Humeniuk, Adam Ramsey, Christopher Strungaru, Nicolae |
| contents | In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffraction of the primes and other sets of zero density Humeniuk, Adam Ramsey, Christopher Strungaru, Nicolae Functional Analysis Number Theory In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types. |
| title | Diffraction of the primes and other sets of zero density |
| topic | Functional Analysis Number Theory |
| url | https://arxiv.org/abs/2406.13687 |