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On the Distribution of Prime Squares and Its Applications — arXiv:2611.00485

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00485
License (as archived): CC0-1.0
Archived: 2026-11-03T11:37:47.240Z
SHA-256 of the archived text: cd7fa422d291baf126ad3948fe108b9f22bad9572667fc2fa5eb7d4ba22061e4
Stable URL of this page: https://metraipolis.com/documento/dc_f2cfd7364bfd

How to cite

On the Distribution of Prime Squares and Its Applications — arXiv:2611.00485 — arXiv (en), https://arxiv.org/abs/2611.00485 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f2cfd7364bfd (Metraipolis archive dc_f2cfd7364bfd, sha256 cd7fa422d291baf126ad3948fe108b9f22bad9572667fc2fa5eb7d4ba22061e4)

BibTeX

@misc{dcf2cfd7364bfd,
  title = {On the Distribution of Prime Squares and Its Applications — arXiv:2611.00485},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00485},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f2cfd7364bfd; sha256 cd7fa422d291baf126ad3948fe108b9f22bad9572667fc2fa5eb7d4ba22061e4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00485. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove that, for every \(A>0\), all but \(O_A(X(\log X)^{-A})\) integers \(n<X\) satisfying \(n\equiv11\pmod{24}\) admit a representation \[ n=a^2+b^2+p^2, \] where \(p\) and \(a^2+b^2+1\) are prime and \((a,b)=1\). For ergodic averages along prime squares, we prove a universal divergence result for integrable functions, while establishing almost-everywhere convergence for near-integrable functions. We also quantify how the bounds used to establish convergence behave as one approaches integrability. Moreover, we prove endpoint improving and sparse bounds for the corresponding discrete averages, with an explicit Orlicz loss.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Number Theory (math.NT) ; Combinatorics (math.CO); Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2611.00485 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T11:05:22.329Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).