{"paper":{"title":"The smallest parts function associated with $\\omega(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Liuquan Wang, Yifan Yang","submitted_at":"2018-12-02T12:15:22Z","abstract_excerpt":"We establish two families of congruences modulo powers of 5 for the Fourier coefficients of $(2E_2(2\\tau)-E_2(\\tau))\\eta(2\\tau)^{-1}$, where $E_2(\\tau)$ is the weight 2 Eisenstein series and $\\eta(\\tau)$ is the Dedekind eta function. This allows us to prove similar congruences for two smallest parts functions. The first function is $\\mathrm{spt}_{\\omega}(n)$, which was introduced by Andrews, Dixit and Yee and associated with Ramanujan/Watson's third order mock theta function $\\omega(q)$. The second one is $\\mathrm{spt}_{C5}(n)$, which appeared in the work of Garvan and Jennings-Shaffer. Moreov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00379","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.00379/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}