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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05333 |
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| _version_ | 1866917608353169408 |
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| author | Gu, Weichen Li, Xiang |
| author_facet | Gu, Weichen Li, Xiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropic van der Corput's Difference Theorem Gu, Weichen Li, Xiang Dynamical Systems Number Theory 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. |
| title | Entropic van der Corput's Difference Theorem |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2403.05333 |