{"paper":{"title":"A Maass Lifting of $\\Theta^3$ and Class Numbers of Real and imaginary Quadratic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Matthias Waldherr, Robert C. Rhoades","submitted_at":"2011-06-01T17:52:14Z","abstract_excerpt":"We give an explicit construct of a harmonic weak Maass form $F_{\\Theta}$ that is a \"lift\" of $\\Theta^3$, where $\\Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $\\Theta^3$ are related to class numbers of imaginary quadratic fields, the Fourier coefficients of the \"holomorphic part\" of $F_{\\Theta}$ are associated to class numbers of real quadratic fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0268","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"}