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arXiv · 2611.04575

Polynomial configurations and pointwise averages along Piatetski--Shapiro primes

Hamed Mousavi
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Abstract

For every \(c>1\) sufficiently close to \(1\), we prove that there is \(κ>0\) such that every sufficiently large \(A\subset[N]\) of density at least \((\log N)^{-κ}\) 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.

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Hamed Mousavi. 2026-11-03. Polynomial configurations and pointwise averages along Piatetski--Shapiro primes. https://arxiv.org/abs/2611.04575

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