The Liouville function in short intervals [after Matomaki and Radziwill]

TL;DR

This paper discusses how the Liouville function demonstrates cancellation in nearly all short intervals as their length increases, based on the work of Matomaki and Radziwill.

Contribution

It presents a summary of Matomaki and Radziwill's results on the Liouville function's behavior in short intervals, highlighting recent advances.

Findings

Liouville function exhibits cancellation in almost all short intervals

Cancellation becomes more pronounced as interval length increases

Supports conjectures about randomness of multiplicative functions

Abstract

This is a copy of my Bourbaki Seminar on the work of Matomaki and Radziwill showing that the Liouville function exhibits cancelation in almost all short intervals as soon as the length of the interval tends to infinity.