{"paper":{"title":"Congruences of Multipartition Functions Modulo Powers of Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Daniel K. Du, Lisa H. Sun, Qing-Hu Hou, William Y. C. Chen","submitted_at":"2012-06-28T11:50:26Z","abstract_excerpt":"Let $p_r(n)$ denote the number of $r$-component multipartitions of $n$, and let $S_{\\gamma,\\lambda}$ be the space spanned by $\\eta(24z)^\\gamma \\phi(24z)$, where $\\eta(z)$ is the Dedekind's eta function and $\\phi(z)$ is a holomorphic modular form in $M_\\lambda({\\rm SL}_2(\\mathbb{Z}))$. In this paper, we show that the generating function of $p_r(\\frac{m^k n +r}{24})$ with respect to $n$ is congruent to a function in the space $S_{\\gamma,\\lambda}$ modulo $m^k$. As special cases, this relation leads to many well known congruences including the Ramanujan congruences of $p(n)$ modulo $5,7,11$ and Ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6642","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"}