Structured extensions and multi-correlation sequences
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912711495909376 |
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| author | Leng, James |
| author_facet | Leng, James |
| contents | We show that every multi-correlation sequence is the sum of a generalized nilsequence and a null-sequence. This proves a conjecture of N. Frantzikinakis. A key ingredient is the reduction of ergodic multidimensional inverse theorems to analogous finitary inverse theorems, offering a new approach to the structure theory of multidimensional Host-Kra factors. This reduction is proven by combining the methods of Tao (2015) with the Furstenberg correspondence principle. We also prove the analogous multidimensional finitary inverse theorem with quasi-polynomial bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured extensions and multi-correlation sequences Leng, James Dynamical Systems Number Theory We show that every multi-correlation sequence is the sum of a generalized nilsequence and a null-sequence. This proves a conjecture of N. Frantzikinakis. A key ingredient is the reduction of ergodic multidimensional inverse theorems to analogous finitary inverse theorems, offering a new approach to the structure theory of multidimensional Host-Kra factors. This reduction is proven by combining the methods of Tao (2015) with the Furstenberg correspondence principle. We also prove the analogous multidimensional finitary inverse theorem with quasi-polynomial bounds. |
| title | Structured extensions and multi-correlation sequences |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2504.07038 |