{"paper":{"title":"Ramanujan Congruences for Fractional Partition Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Erin Bevilacqua, Kapil Chandran, Yunseo Choi","submitted_at":"2019-07-15T19:46:28Z","abstract_excerpt":"For rational $\\alpha$, the fractional partition functions $p_\\alpha(n)$ are given by the coefficients of the generating function $(q;q)^\\alpha_\\infty$. When $\\alpha=-1$, one obtains the usual partition function. Congruences of the form $p(\\ell n + c)\\equiv 0 \\pmod{\\ell}$ for a prime $\\ell$ and integer $c$ were studied by Ramanujan. Such congruences exist only for $\\ell\\in\\{5,7,11\\}.$ Chan and Wang [4] recently studied congruences for the fractional partition functions and gave several infinite families of congruences using identities of the Dedekind eta-function. Following their work, we use t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06716","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"}