{"paper":{"title":"A quantitative improvement for Roth's theorem on arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Thomas F. Bloom","submitted_at":"2014-05-22T15:41:58Z","abstract_excerpt":"We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showing that if $A\\subset\\{1,\\ldots,N\\}$ contains no non-trivial three-term arithmetic progressions then $\\lvert A\\rvert\\ll N(\\log\\log N)^4/\\log N$. By the same method we also improve the bounds in the analogous problem over $\\mathbb{F}_q[t]$ and for the problem of finding long arithmetic progressions in a sumset."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5800","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}