Everywhere divergence of the one-sided ergodic Hilbert transform and Liouville numbers

David Constantine, Joanna Furno

We prove some results on the behavior of infinite sums of the form $\Sigma f\circ T^n(x)\frac{1}{n}$, where $T:S^1\to S^1$ is an irrational circle rotation and $f$ is a mean-zero functio…