{"paper":{"title":"A continuous model for systems of complexity 2 on simple abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Szegedy, Pablo Candela","submitted_at":"2015-09-15T10:39:27Z","abstract_excerpt":"It is known that if $p$ is a sufficiently large prime then for every function $f:\\mathbb{Z}_p\\to [0,1]$ there exists a continuous function on the circle $f':\\mathbb{T}\\to [0,1]$ such that the averages of $f$ and $f'$ across any prescribed system of linear forms of complexity 1 differ by at most $\\epsilon$. This result follows from work of Sisask, building on Fourier-analytic arguments of Croot that answered a question of Green. We generalize this result to systems of complexity at most 2, replacing $\\mathbb{T}$ with the torus $\\mathbb{T}^2$ equipped with a specific filtration. To this end we u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04485","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"}