Note on the Theory of Correlation Functions

TL;DR

This paper aims to enhance the theoretical understanding of the correlation functions associated with the Möbius and Liouville sequences, which are important in number theory.

Contribution

It provides improved theoretical results concerning the correlation functions of the Möbius and Liouville sequences, advancing the mathematical understanding of these sequences.

Findings

Enhanced bounds for correlation functions of Möbius sequence

Improved estimates for correlation functions of Liouville sequence

Contributions to the theoretical framework of multiplicative functions

Abstract

The purpose of this note is to improve the current theoretical results for the correlation functions of the Mobius sequence $\{\mu(n): n\geq 1 \}$ and the Liouville sequence $\{\lambda(n): n\geq 1 \}$.