A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts 1nαºof the sequence (nα)n≥1 are uniformly distributed in the unit interval whenever α > 0 is not an integer. For sharpening this knowledge to local statistics, the k-level correlation functions of the sequence (1nαº)n≥1 are of fundamental importance. We prove that for each k ≥ 2; the k-level correlation function Rk is Poissonian for almost every α > 4k2 - 4k - 1.
- Uniform distribution modulo 1
- correlation functions
- local statistics
All Science Journal Classification (ASJC) codes
- Applied Mathematics