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arXiv · 2609.01847

Polynomial configurations and pointwise averages along Piatetski-Shapiro sequences

Hamed Mousavi
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Abstract

In this paper, we prove that for every integer $k\geq2$ and every $c>1$ sufficiently close to $1$, there is $κ>0$ such that every sufficiently large subset of $\{1,\ldots,N\}$ of density at least $(\log\log N)^{-κ}$ contains \[ x,\quad x+\lfloor n^c\rfloor,\quad x+\lfloor n^c\rfloor^2, \quad\ldots,\quad x+\lfloor n^c\rfloor^k. \] We also prove pointwise almost-everywhere convergence of the associated multiple ergodic averages.

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Hamed Mousavi. 2026-09-01. Polynomial configurations and pointwise averages along Piatetski-Shapiro sequences. https://arxiv.org/abs/2609.01847

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