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Polynomial configurations and pointwise averages along Piatetski--Shapiro primes
Abstract
For every c>1 sufficiently close to 1, we prove that there is κ>0 such that every sufficiently large A⊂[N] of density at least (log N)−κ contains x, x+(p−1), x+(p−1)2,…, x+(p−1)k, p=⌊ nc⌋∈ℙ. We also prove pointwise almost-everywhere convergence of the corresponding multiple ergodic averages.
Related
- Polynomial configurations and pointwise averages along Piatetski-Shapiro sequences
- Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets
- On a variant of the Piatetski-Shapiro prime number theorem
- Linear equations in Piatetski-Shapiro primes
- Better than square-root cancellation and Gaussian behavior on Piatetski-Shapiro Sequences
BibTeX
@misc{mousavi2026polynomial,
title = {{Polynomial configurations and pointwise averages along Piatetski--Shapiro primes}},
author = {Hamed Mousavi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04575},
eprint = {2611.04575},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04575},
}
RIS
TY - UNPB
TI - Polynomial configurations and pointwise averages along Piatetski--Shapiro primes
AU - Hamed Mousavi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04575
UR - https://arxiv.org/abs/2611.04575
AB - For every c>1 sufficiently close to 1, we prove that there is κ>0 such that every sufficiently large A⊂[N] of density at least (log N)^−κ contains x, x+(p−1), x+(p−1)^2,…, x+(p−1)^k, p=⌊ n^c⌋∈ℙ. We also prove pointwise almost-everywhere convergence of the corresponding multiple ergodic averages.
ER -