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arXiv · 2001.11523

A decomposition of multicorrelation sequences for commuting transformations along primes

Anh N. Le·Joel Moreira·Florian K. Richter
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Abstract

We study multicorrelation sequences arising from systems with commuting transformations. Our main result is a refinement of a decomposition result of Frantzikinakis and it states that any multicorrelation sequences for commuting transformations can be decomposed, for every $ε>0$, as the sum of a nilsequence $ϕ(n)$ and a sequence $ω(n)$ satisfying $\lim_{N\to\infty}\frac{1}{N}\sum_{n=1}^N |ω(n)|<ε$ and $\lim_{N\to\infty}\frac{1}{|\mathbb{P}\cap [N]|}\sum_{p\in \mathbb{P}\cap [N]} |ω(p)|<ε$.

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Anh N. Le, Joel Moreira, Florian K. Richter. 2021-06-07. A decomposition of multicorrelation sequences for commuting transformations along primes. https://doi.org/10.19086/da.22056

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