On Correlations of Liouville-like Functions

2023/12/10 by You, Yichen
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.06012

Abstract

Let A be a set of mutually coprime positive integers, satisfying ∑_a\inA(1)/(a) = ∞. Define the (possibly non-multiplicative) "Liouville-like" functions λ_A(n) = (-1)^#\a:a|n, a ∈ A\ or (-1)^#\a:a^ν∥ n, a ∈ A, ν∈ ℕ\. We show that lim_x→∞(1)/(x)∑_{n ≤ x} λ_A(n) = 0 holds, answering a question of de la Rue.

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