{"paper":{"title":"Ramanujan-type Congruences for Overpartitions Modulo 16","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Lisa H. Sun, Li Zhang, Qing-Hu Hou, William Y.C. Chen","submitted_at":"2014-08-07T14:03:56Z","abstract_excerpt":"Let $\\overline{p}(n)$ denote the number of overpartitions of $n$. Recently, Fortin-Jacob-Mathieu and Hirschhorn-Sellers independently obtained 2-, 3- and 4-dissections of the generating function for $\\overline{p}(n)$ and derived a number of congruences for $\\overline{p}(n)$ modulo $4$, $8$ and $64$ including $\\overline{p}(5n+2)\\equiv 0 \\pmod{4}$, $\\overline{p}(4n+3)\\equiv 0 \\pmod{8}$ and $\\overline{p}(8n+7)\\equiv 0 \\pmod{64}$. By employing dissection techniques, Yao and Xia obtained congruences for $\\overline{p}(n)$ modulo $8, 16$ and $32$, such as $\\overline{p}(48n+26) \\equiv 0 \\pmod{8}$, $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1597","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"}