{"paper":{"title":"On the asymptotic maximal density of a set avoiding solutions to linear equations modulo a prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Olof Sisask, Pablo Candela","submitted_at":"2011-09-13T21:17:23Z","abstract_excerpt":"Given a finite family F of linear forms with integer coefficients, and a compact abelian group G, an F-free set in G is a measurable set which does not contain solutions to any equation L(x)=0 for L in F. We denote by d_F(G) the supremum of m(A) over F-free sets A in G, where m is the normalized Haar measure on G. Our main result is that, for any such collection F of forms in at least three variables, the sequence d_F(Z_p) converges to d_F(R/Z) as p tends to infinity over primes. This answers an analogue for Z_p of a question that Ruzsa raised about sets of integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2934","kind":"arxiv","version":1},"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"}