{"paper":{"title":"An inverse theorem for the uniformity seminorms associated with the action of $F^\\omega$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Tamar Ziegler, Terence Tao, Vitaly Bergelson","submitted_at":"2009-01-17T01:11:01Z","abstract_excerpt":"Let $\\F$ a finite field. We show that the universal characteristic factor for the Gowers-Host-Kra uniformity seminorm $U^k(\\X)$ for an ergodic action $(T_g)_{g \\in \\F^\\omega}$ of the infinite abelian group $\\F^\\omega$ on a probability space $X = (X,\\B,\\mu)$ is generated by phase polynomials $\\phi: X \\to S^1$ of degree less than $C(k)$ on $X$, where $C(k)$ depends only on $k$. In the case where $k \\leq \\charac(\\F)$ we obtain the sharp result $C(k)=k$. This is a finite field counterpart of an analogous result for $\\Z$ by Host and Kra. In a companion paper to this paper, we shall combine this res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2602","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"}