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Autocorrelation of the Mobius Function
- Publication Year :
- 2022
-
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.<br />Comment: Eight Pages. Keywords: Autocorrelation; Correlation; Arithmetic function; Mobius function; Liouville function; Chola conjecture
- Subjects :
- Mathematics - General Mathematics
Primary 11N37, Secondary 11P32
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2202.01071
- Document Type :
- Working Paper