{"paper":{"title":"Large values of the Gowers-Host-Kra seminorms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DS"],"primary_cat":"math.CO","authors_text":"Tanja Eisner, Terence Tao","submitted_at":"2010-12-16T03:43:24Z","abstract_excerpt":"The \\emph{Gowers uniformity norms} $\\|f\\|_{U^k(G)}$ of a function $f: G \\to \\C$ on a finite additive group $G$, together with the slight variant $\\|f\\|_{U^k([N])}$ defined for functions on a discrete interval $[N] := \\{1,...,N\\}$, are of importance in the modern theory of counting additive patterns (such as arithmetic progressions) inside large sets. Closely related to these norms are the \\emph{Gowers-Host-Kra seminorms} $\\|f\\|_{U^k(X)}$ of a measurable function $f: X \\to \\C$ on a measure-preserving system $X = (X, {\\mathcal X}, \\mu, T)$. Much recent effort has been devoted to the question of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3509","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"}