A note on the Liouville function in short intervals

Kaisa Matomäki, Maksym Radziwiłł

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 g…