N. Tardy

Two-point correlations of multiplicative functions with dense orbits

Let $f,g:\mathbb{N}\to\mathbb{T}$ be completely multiplicative functions with dense images in the complex unit circle $\mathbb{T}$. We prove that, for every non-empty open set $U \subset \mathbb{T}^2$, the set of integers $n$ such that $(f(n),g(n+1)) \in U$ has positive lower logarithmic density, unless the pair $(f,g)...