{"paper":{"title":"A note on sumsets of subgroups in $\\mathbb Z_p^*$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Derrick Hart","submitted_at":"2013-03-12T00:15:39Z","abstract_excerpt":"Let $A$ be a multiplicative subgroup of $\\mathbb Z_p^*$. Define the $k$-fold sumset of $A$ to be $kA=\\{x_1+\\dots+x_k:x_i \\in A,1\\leq i\\leq k\\}$. We show that $6A\\supseteq \\mathbb Z_p^*$ for $|A| > p^{\\frac {11}{23} +\\epsilon}$. In addition, we extend a result of Shkredov to show that $|2A|\\gg |A|^{\\frac 85-\\epsilon}$ for $|A|\\ll p^{\\frac 59}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2729","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"}