{"paper":{"title":"A classification of harmonic Maass forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kathrin Bringmann, Stephen Kudla","submitted_at":"2016-09-22T14:39:39Z","abstract_excerpt":"We give a classification of the Harish-Chandra modules generated by the pullback to $\\text{SL}_2(\\mathbb R)$ of harmonic Maass forms for congruence subgroups of $\\text{SL}_2(\\mathbb Z)$ with exponential growth allowed at the cusps. We assume that the weight is integral but include vector-valued forms. Due to the weak growth condition, these modules need not be irreducible. Elementary Lie algebra considerations imply that there are 9 possibilities, and we show, by giving explicit examples, that all of them arise from harmonic Maass forms. Finally, we briefly discuss the case of forms that are n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06999","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"}