The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures

Terence Tao, Joni Teräväinen

We study the asymptotic behaviour of higher order correlations $${\mathbb{E}}_{n\le X/d}{g}_1(n+a{h}_1)\cdots g_k(n+a{h}_k)$$ as a function of the parameters $a$ and $d$, where $g_1,\…