Perturbed Polynomial Powers and Bourgain Entropy Obstructions for Khintchin Averages

Zhuowen Guo, Shuhao Zhang

Let $a\ge 2$, let $p\in \mathbb{Z}[n]$ be eventually increasing and eventually non-negative, and let ${\lambda }_n=a^{p(n)}+f(n)>0$, where $f(n)\in \mathbb{Z}$. We prove, using Bourgain's boun…