Squarefrees are Gaussian in short intervals - Gorodetsky, O; Mangerel, A; Rodgers, B (De Gruyter, 2022)
We show that counts of squarefree integers up to X in short intervals of size H tend to a Gaussian distribution as long as H→∞  and H=Xo(1). This answers a question posed by R. R. Hall in 1989. More generally, we prove a variant of Donsker’s theorem, showing that these counts scale to a fractional Brownian motion with Hurst parameter 1/4. In fact, we are able to prove these results hold in general for collections of B-free integers as long as the sieving set B satisfies a very mild regularity property, for Hurst parameter varying with the set B.