{"paper":{"title":"Classification of congruences for mock theta functions and weakly holomorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nickolas Andersen","submitted_at":"2013-06-30T02:00:25Z","abstract_excerpt":"Let $f(q)$ denote Ramanujan's mock theta function \\[f(q) = \\sum_{n=0}^{\\infty} a(n) q^{n} := 1+\\sum_{n=1}^{\\infty} \\frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\\cdots(1+q^{n})^{2}}.\\] It is known that there are many linear congruences for the coefficients of $f(q)$ and other mock theta functions. We prove that if the linear congruence $a(mn+t) \\equiv 0 \\pmod{\\ell}$ holds for some prime $\\ell \\geq 5$, then $\\ell | m$ and $(\\frac{24t-1}{\\ell}) \\neq (\\frac{-1}{\\ell})$. We prove analogous results for the mock theta function $\\omega(q)$ and for a large class of weakly holomorphic modular forms which incl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0169","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"}