{"paper":{"title":"Sums of dilates in $\\mathbb{Z}_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gonzalo Fiz Pontiveros","submitted_at":"2012-03-12T21:33:25Z","abstract_excerpt":"We consider the problem of sums of dilates in groups of prime order. We show that given $A\\subset \\Z{p}$ of sufficiently small density then $$\\big| \\lambda_{1}A+\\lambda_{2}A+...+ \\lambda_{k}A \\big| \\,\\ge\\,\\bigg(\\sum_{i}|\\lambda_{i}|\\bigg)|A|- o(|A|),$$ whereas on the other hand, for any $\\epsilon>0$, we construct subsets of density $1/2-\\epsilon$ such that $|A+\\lambda A|\\leq (1-\\delta)p$, showing that there is a very different behaviour for subsets of large density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2659","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"}