{"paper":{"title":"Any small multiplicative sugroup is not a sumset","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Ilya D. Shkredov","submitted_at":"2017-02-03T22:54:20Z","abstract_excerpt":"We prove that for an arbitrary $\\varepsilon>0$ and any multiplicative subgroup $\\Gamma \\subseteq \\mathbf{F}_p$, $1\\ll |\\Gamma| \\le p^{2/3 -\\varepsilon}$ there are no sets $B$, $C \\subseteq \\mathbf{F}_p$ with $|B|, |C|>1$ such that $\\Gamma=B+C$. Also, we obtain that for $1\\ll |\\Gamma| \\le p^{6/7-\\varepsilon}$ and any $\\xi\\neq 0$ there is no a set $B$ such that $\\xi \\Gamma+1=B/B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01197","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"}