论文标题
多相关序列的分解，用于通勤沿素数
A decomposition of multicorrelation sequences for commuting transformations along primes
论文作者
论文摘要
我们研究由通勤转换的系统产生的多相关序列。我们的主要结果是对Frantzikinakis的分解结果的完善，它指出，对于每$ε> 0 $，可以分解用于通勤转换的任何多相关序列，作为nilsequence $ ϕ（n）$和序列$ω（n）$满意的nilsequence $ ϕ（n）$的总和$ \ lim_ {n \ to \ infty} \ frac {1} {n} \ sum_ {n = 1}^n |ω（n）| <ε$和$ \ lim_ {n \ to \ infty} \ Mathbb {p} \ cap [n]} |ω（p）| <ε$。
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 $\lim_{N\to\infty}\frac{1}{|\mathbb{P}\cap [N]|}\sum_{p\in \mathbb{P}\cap [N]} |ω(p)|<ε$.
