Autocorrelation of the Mobius Function

2022/01/31 by N. A. Carella, Carella, N. A.
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #Primary 11N37 #Secondary 11P32

paper · pdf · doi:10.48550/arxiv.2202.01071

openalex publication_date 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let x≥ 1 be a large integer, and let μ:ℕ\longrightarrow\-1,0,1\ be the Mobius function. This article proposes an effective asymptotic result for the autocorrelation function ∑_{n ≤ x} μ(n) μ(n+t) =O( e^{-c√(log x)}) , where t≠ 0 be a small fixed integer, and c>0 is a constant.

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