Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866913235261718528 |
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| author | Manners, Frederick |
| author_facet | Manners, Frederick |
| contents | We provide a new proof of the inverse theorem for the Gowers $U^{s+1}$-norm over groups $H=\mathbb Z/N\mathbb Z$ for $N$ prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular does not make use of regularity or non-standard analysis, both of which are new for $s \ge 3$ in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_00718 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups Manners, Frederick Combinatorics Number Theory We provide a new proof of the inverse theorem for the Gowers $U^{s+1}$-norm over groups $H=\mathbb Z/N\mathbb Z$ for $N$ prime. This proof gives reasonable quantitative bounds (the worst parameters are double-exponential), and in particular does not make use of regularity or non-standard analysis, both of which are new for $s \ge 3$ in this setting. |
| title | Quantitative bounds in the inverse theorem for the Gowers $U^{s+1}$-norms over cyclic groups |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/1811.00718 |