Year: 2026
Type: preprint
Abstract: Let $f\colon\mathbb{N}\to\mathbb{U}$ be a non-pretentious multiplicative function in the sense of Granville and Soundararajan. We study the convergence of the autocorrelation averages of $f$. In particular, we investigate the relationship between the local pretentious behaviour of $f$ on intervals of the form $[x^{\varepsilon},x]$ and its deviation from $1$ on the primes. As an application, we exhibit a class of non-pretentious multiplicative functions for which Elliott's conjecture in its original formulation holds, following up on a result by Klurman, Mangerel and Teräväinen.
Source: arXiv (Cornell University)
Author: Renard, Thomas
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214955966