Autocorrelation of the Mobius Function

N. A. Carella

Autocorrelation of the Mobius Function

General Mathematics 2023-11-20 v5

Authors: N. A. Carella

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.

Keywords

multiplicative functions

Cite

@article{arxiv.2202.01071,
  title  = {Autocorrelation of the Mobius Function},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:2202.01071},
  year   = {2023}
}