Efficient equidistribution of periodic nilsequences and applications
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916141208698880 |
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| author | Leng, James |
| author_facet | Leng, James |
| contents | This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinatorics. The first application is quasi-polynomial bounds for a certain complexity one polynomial progression, improving the iterated logarithm bound previusly obtained. The second application is a proof of the quasi-polynomial $U^4[N]$ inverse theorem. In work with Sah and Sawhney, we obtain improved bounds for sets lacking nontrivial $5$-term arithmetic progressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13820 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient equidistribution of periodic nilsequences and applications Leng, James Number Theory Classical Analysis and ODEs Combinatorics Dynamical Systems This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinatorics. The first application is quasi-polynomial bounds for a certain complexity one polynomial progression, improving the iterated logarithm bound previusly obtained. The second application is a proof of the quasi-polynomial $U^4[N]$ inverse theorem. In work with Sah and Sawhney, we obtain improved bounds for sets lacking nontrivial $5$-term arithmetic progressions. |
| title | Efficient equidistribution of periodic nilsequences and applications |
| topic | Number Theory Classical Analysis and ODEs Combinatorics Dynamical Systems |
| url | https://arxiv.org/abs/2306.13820 |