Fast and slow points of Birkhoff sums

Frédéric Bayart, Zoltan Buczolich, Yanick Heurteaux

We investigate the growth rate of the Birkhoff sums $S_{n,\alpha }f(x)={\sum }_{k=0}^{n-1}f(x+k\alpha )$, where $f$ is a continuous function with zero mean defined on the unit circle $\mathbb T…