Control and its applications in additive combinatorics
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909457825398784 |
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| author | Bloom, Thomas F. |
| author_facet | Bloom, Thomas F. |
| contents | We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we improve the known bounds for the sum-product problem, the Balog-Szemerédi-Gowers theorem, and the additive growth of convex sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control and its applications in additive combinatorics Bloom, Thomas F. Number Theory Combinatorics We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we improve the known bounds for the sum-product problem, the Balog-Szemerédi-Gowers theorem, and the additive growth of convex sets. |
| title | Control and its applications in additive combinatorics |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2501.09470 |