Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916351907463168 |
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| author | Leng, James Sah, Ashwin Sawhney, Mehtaab |
| author_facet | Leng, James Sah, Ashwin Sawhney, Mehtaab |
| contents | We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution of nilsequences. In a companion paper, this result will be used to improve the bounds on Szemerédi's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm Leng, James Sah, Ashwin Sawhney, Mehtaab Combinatorics Dynamical Systems Number Theory We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input recent work of the first author regarding the equidistribution of nilsequences. In a companion paper, this result will be used to improve the bounds on Szemerédi's theorem. |
| title | Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm |
| topic | Combinatorics Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2402.17994 |