Abstract:
A well known result due to Koksma states that for Lebesgue almost every x>1 the sequence (x^n) is uniformly distributed modulo 1. In this talk I will discuss a recent refinement of this result. Namely that for Lebesgue almost every x>1 the sequence (x^n) has Poisonnian pair correlations. This is based upon some joint work with Christoph Aistleitner.