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Polynomial configurations and pointwise averages along Piatetski--Shapiro primes — arXiv:2611.04575

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04575
License (as archived): CC0-1.0
Archived: 2026-11-04T12:48:48.129Z
SHA-256 of the archived text: ffb34df4de719b650dede3c14d6a262333e7d2f6dc06e256c01f1eb581d2d866
Stable URL of this page: https://metraipolis.com/documento/dc_960bf7dedd73

How to cite

Polynomial configurations and pointwise averages along Piatetski--Shapiro primes — arXiv:2611.04575 — arXiv (en), https://arxiv.org/abs/2611.04575 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_960bf7dedd73 (Metraipolis archive dc_960bf7dedd73, sha256 ffb34df4de719b650dede3c14d6a262333e7d2f6dc06e256c01f1eb581d2d866)

BibTeX

@misc{dc960bf7dedd73,
  title = {Polynomial configurations and pointwise averages along Piatetski--Shapiro primes — arXiv:2611.04575},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04575},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_960bf7dedd73; sha256 ffb34df4de719b650dede3c14d6a262333e7d2f6dc06e256c01f1eb581d2d866},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04575. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For every \(c>1\) sufficiently close to \(1\), we prove that there is \(\kappa>0\) such that every sufficiently large \(A\subset[N]\) of density at least \((\log N)^{-\kappa}\) contains \[ x,\ x+(p-1),\ x+(p-1)^2,\ldots,\ x+(p-1)^k, \qquad p=\lfloor n^c\rfloor\in\mathbb P. \] We also prove pointwise almost-everywhere convergence of the corresponding multiple ergodic averages.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Dynamical Systems (math.DS); Number Theory (math.NT).
Pagina del lavoro: https://arxiv.org/abs/2611.04575 — 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 2026-11-04T12:32:32.032Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).