# Fully oscillating sequences and weighted multiple ergodic limit

## TL;DR

This paper proves that fully oscillating sequences are orthogonal to multiple ergodic realizations of zero entropy affine maps on compact abelian groups, extending the implications of Sarnak's conjecture for these systems.

## Contribution

It establishes a stronger orthogonality result for fully oscillating sequences in the context of zero entropy affine dynamical systems.

## Key findings

- Fully oscillating sequences are orthogonal to multiple ergodic affine maps.
- The result exceeds the requirements of Sarnak's conjecture for these systems.
- Provides new insights into the behavior of oscillating sequences in ergodic theory.

## Abstract

We prove that fully oscillating sequences are orthogonal to multiple ergodic realizations of affine maps of zero entropy on compact abelian groups. It is more than what Sarnak's conjecture requires for these dynamical systems.