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arXiv · 2403.05333

Entropic van der Corput's Difference Theorem

Weichen Gu·Xiang Li
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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.

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Weichen Gu, Xiang Li. 2024-03-08. Entropic van der Corput's Difference Theorem. https://arxiv.org/abs/2403.05333

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