Year: 2026
Type: preprint
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 upper 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 simpler proofs.
Source: arXiv (Cornell University)
Author: Tardy, Néo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204584707