English

Entropic van der Corput's Difference Theorem

Dynamical Systems 2024-03-11 v1 Number Theory

Abstract

We prove an entropy version of van der Corput's difference theorem: the entropy of a sequence is equal to the entropy of its differences. This reveals a potential correspondence between the theory of uniform distribution mod 1 and entropy. As applications, we establish the corresponding entropy versions for several other results on uniform distribution.

Keywords

Cite

@article{arxiv.2403.05333,
  title  = {Entropic van der Corput's Difference Theorem},
  author = {Weichen Gu and Xiang Li},
  journal= {arXiv preprint arXiv:2403.05333},
  year   = {2024}
}
R2 v1 2026-06-28T15:13:37.892Z