{"paper":{"title":"Intersections of sets of distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mauro Di Nasso","submitted_at":"2014-10-15T08:48:38Z","abstract_excerpt":"We isolate conditions on the relative size of sets of natural numbers $A,B$ that guarantee a nonempty intersection $\\Delta(A)\\cap\\Delta(B)\\ne\\emptyset$ of the corresponding sets of distances. Such conditions apply to a large class of zero density sets. We also show that a variant of Khintchine's Recurrence Theorem holds for all infinite sets $A=\\{a_1<a_2<...\\}$ with $a_n\\ll n^{3/2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3973","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"}