# Correlations of multiplicative functions along deterministic and independent sequences

## TL;DR

This paper investigates the correlations of multiplicative functions along both deterministic and independent sequences, employing ergodic theory to extend recent results and analyze structural properties of measure-preserving systems.

## Contribution

It introduces a novel ergodic theory approach to study multiplicative functions along sequences, extending previous work by Tao, Teräväinen, and the author.

## Key findings

- Extended correlations results for multiplicative functions
- Utilized ergodic theory to analyze deterministic sequences
- Applied multiple ergodic theorems to independent sequences

## Abstract

We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained extend recent results of Tao and Ter\"av\"ainen and results of the author. Our approach is to use tools from ergodic theory in order to effectively exploit feedback from analytic number theory. The results on deterministic sequences crucially use structural properties of measure preserving systems associated with bounded multiplicative functions that were recently obtained by the author and Host. The results on independent sequences depend on multiple ergodic theorems obtained using the theory of characteristic factors and qualitative equidistribution results on nilmanifolds.