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arXiv · 2609.37332

Truncated pretentious distances of multiplicative arithmetic functions

Thomas Renard
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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.

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Thomas Renard. 2026-09-29. Truncated pretentious distances of multiplicative arithmetic functions. https://arxiv.org/abs/2609.37332

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