{"paper":{"title":"Fourier uniformity on subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Ben Green, Tom Sanders","submitted_at":"2015-10-29T15:28:47Z","abstract_excerpt":"Let $\\mathbb{F}$ be a fixed finite field, and let $A \\subset \\mathbb{F}^n$. It is a well-known fact that there is a subspace $V \\leq \\mathbb{F}^n$, $\\mbox{codim} V \\ll_{\\delta} 1$, and an $x$, such that $A$ is $\\delta$-uniform when restricted to $x + V$ (that is, all non-trivial Fourier coefficients of $A$ restricted to $x + V$ have magnitude at most $\\delta$). We show that if $\\mathbb{F} = \\mathbb{F}_2$ then it is possible to take $x = 0$; that is, $A$ is $\\delta$-uniform on a subspace $V \\leq \\mathbb{F}^n$. We give an example to show that this is not necessarily possible when $\\mathbb{F} = \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08739","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"}