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.
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}
}