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arXiv · 2202.01071

Autocorrelation of the Mobius Function

N. A. Carella
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Abstract

Let $x\geq 1$ be a large integer, and let $\mu:\mathbb{N}\longrightarrow\{-1,0,1\}$ be the Mobius function. This article proposes an effective asymptotic result for the autocorrelation function $\sum_{n \leq x} \mu(n) \mu(n+t) =O\left( e^{-c\sqrt{\log x}}\right) $, where $t\ne 0$ be a small fixed integer, and $c>0$ is a constant.

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N. A. Carella. 2022-01-31. Autocorrelation of the Mobius Function. https://arxiv.org/abs/2202.01071

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