A note on the Liouville function in short intervals

Abstract

In this note we give a short and self-contained proof that, for any $\delta >0$, ${\sum }_{x\le n\le x+x^{\delta }}\lambda (n)=o(x^{\delta })$ for almost all $x\in [X,2X]$. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print.

12 pages, expository note

Cited by in corpus (1)

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