论文标题
在多项式上，均匀的千古双线性与liouville和möbius重量
On the polynomials homogeneous ergodic bilinear averages with Liouville and Möbius weights
论文作者
论文摘要
我们通过证明在概率空间$（x，x，\ mathcal {a}，μ）上的任何映射$ t $来建立对波尔加因双重复发定理的概括，以及任何非恒定多项式$ p，q $ p，q $ p，q $ in lys $ f，in l^in^2（x）$ x（x）$ x（x）$ x（所有） $ \ lim _ {\ bar {n} \ longrightArrow +\ infty} \ frac {1} {n} {n} \ sum_ {n = 1}^{n} \boldsymbol务功能或Möbius的功能。
We establish a generalization of Bourgain double recurrence theorem by proving that for any map $T$ acting on a probability space $(X,\mathcal{A},μ)$, and for any non-constant polynomials $P, Q$ mapping natural numbers to themselves, for any $f,g \in L^2(X)$, and for almost all $x \in X$, we have $$\lim_{\bar{N} \longrightarrow +\infty} \frac{1}{N} \sum_{n=1}^{N}\boldsymbolν(n) f(T^{P(n)}x)g(T^{Q(n)}x)=0$$ where $\boldsymbolν$ is the Liouville function or the Möbius¶ function.
