{"paper":{"title":"Hecke-type congruences for two smallest parts functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nickolas Andersen","submitted_at":"2012-09-18T16:12:19Z","abstract_excerpt":"We prove infinitely many congruences modulo 3, 5, and powers of 2 for the overpartition function $\\bar{p}(n)$ and two smallest parts functions: $\\bar{\\operatorname{spt1}}(n)$ for overpartitions and $\\operatorname{M2spt}(n)$ for partitions without repeated odd parts. These resemble the Hecke-type congruences found by Atkin for the partition function $p(n)$ in 1966 and Garvan for the smallest parts function $\\operatorname{spt}(n)$ in 2010. The proofs depend on congruences between the generating functions for $\\bar{p}(n)$, $\\bar{\\operatorname{spt1}}(n),$ and $\\operatorname{M2spt}(n)$ and eigenfor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4009","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"}