Van der Corput and metric theorems for geometric progressions for self-similar measures

Amir Algom, Yuanyang Chang, Meng Wu +1

We prove a van der Corput lemma for non-atomic self-similar measures $\mu$. As an application, we show that the correlations of all finite orders of $(x^n\mathrm{mod}1{)}_{n\ge 1}$ conver…