{"paper":{"title":"Ramanujan-type Congruences for Overpartitions Modulo 5","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, Rong-Hua Wang, William Y.C. Chen","submitted_at":"2014-06-15T08:29:45Z","abstract_excerpt":"Let $\\overline{p}(n)$ denote the number of overpartitions of $n$. Hirschhorn and Sellers showed that $\\overline{p}(4n+3)\\equiv 0 \\pmod{8}$ for $n\\geq 0$. They also conjectured that $\\overline{p}(40n+35)\\equiv 0 \\pmod{40}$ for $n\\geq 0$. Chen and Xia proved this conjecture by using the $(p,k)$-parametrization of theta functions given by Alaca, Alaca and Williams. In this paper, we show that $\\overline{p}(5n)\\equiv (-1)^{n}\\overline{p}(4\\cdot 5n) \\pmod{5}$ for $n \\geq 0$ and $\\overline{p}(n)\\equiv (-1)^{n}\\overline{p}(4n)\\pmod{8}$ for $n \\geq 0$ by using the relation of the generating function o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3801","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"}