{"paper":{"title":"An application of kissing numbers in sum-product estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ching Wong, Jozsef Solymosi","submitted_at":"2017-09-26T00:10:24Z","abstract_excerpt":"The boundedness of the kissing numbers of convex bodies has been known to Hadwiger for long. We present an application of it to the sum-product estimate $$\\max(|\\mathcal{A}+\\mathcal{A}|,|\\mathcal{A}\\mathcal{A}|)\\gg\\dfrac{|\\mathcal{A}|^{4/3}}{\\lceil\\log|\\mathcal{A}|\\rceil^{1/3}}$$ for finite sets $\\mathcal{A}$ of quaternions and of a certain family of well-conditioned matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08758","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"}