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arXiv · 2608.26814

Two-point correlations of multiplicative functions with dense orbits

Néo Tardy
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Abstract

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 $(f,g)$ is of a special form. This result strengthens earlier theorems of Klurman and Mangerel, as well as of Charamaras, Mountakis, and Tsinas, and yields substantially simpler proofs.

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Néo Tardy. 2026-08-27. Two-point correlations of multiplicative functions with dense orbits. https://arxiv.org/abs/2608.26814

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