{"paper":{"title":"The inverse conjecture for the Gowers norm over finite fields in low characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tamar Ziegler, Terence Tao","submitted_at":"2011-01-07T16:45:30Z","abstract_excerpt":"We establish the \\emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \\to \\C$ on a finite-dimensional vector space $V$ over a finite field $\\F$ has large Gowers uniformity norm $\\|f\\|_{U^{s+1}(V)}$, then there exists a (non-classical) polynomial $P: V \\to \\T$ of degree at most $s$ such that $f$ correlates with the phase $e(P) = e^{2\\pi i P}$. This conjecture had already been established in the \"high characteristic case\", when the characteristic of $\\F$ is at least as large as $s$. Our proof relies on the weak form o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1469","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"}