论文标题
具有整数部分多项式迭代的多相关序列的结构沿素数
Structure of multicorrelation sequences with integer part polynomial iterates along primes
论文作者
论文摘要
令$ t $为保存$ \ mathbb {z}^\ ell $ - 概率空间$（x，{\ Mathcal b}，μ），$ $ q_1，\ dots，q_m：{\ Mathbb r} $ f_0，\ dots，f_m \ in l^\ infty（x）$。对于任何$ε> 0 $和形式的多相关序列$ \ displaystyle \ lim_ {n -m \ to \ infty} \ frac {1} {n -m} {n -m} \ sum_ {n = m}^{n -1}^{n -1} |α（n） - \leqε$和$ \ displayStyle \ lim_ {n \ to \ infty} \ frac {1} {π（n）} \ sum_ {p \ in {\ mathbb p} \ cap [1，n]，n]} \leqε。$此结果同时概括了Frantzikinakis [2]和作者[11,13]的先前结果。
Let $T$ be a measure preserving $\mathbb{Z}^\ell$-action on the probability space $(X,{\mathcal B},μ),$ $q_1,\dots,q_m:{\mathbb R}\to{\mathbb R}^\ell$ vector polynomials, and $f_0,\dots,f_m\in L^\infty(X)$. For any $ε> 0$ and multicorrelation sequences of the form $\displaystyleα(n)=\int_Xf_0\cdot T^{ \lfloor q_1(n) \rfloor }f_1\cdots T^{ \lfloor q_m(n) \rfloor }f_m\;dμ$ we show that there exists a nilsequence $ψ$ for which $\displaystyle\lim_{N - M \to \infty} \frac{1}{N-M} \sum_{n=M}^{N-1} |α(n) - ψ(n)| \leq ε$ and $\displaystyle\lim_{N \to \infty} \frac{1}{π(N)} \sum_{p \in {\mathbb P}\cap[1,N]} |α(p) - ψ(p)| \leq ε.$ This result simultaneously generalizes previous results of Frantzikinakis [2] and the authors [11,13].
