{"paper":{"title":"An identity connecting theta series associated with binary quadratic forms of discriminant $\\Delta$ and $\\Delta($prime$)^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frank Patane","submitted_at":"2014-09-22T18:57:24Z","abstract_excerpt":"We state and prove an identity which connects theta series associated with binary quadratic forms of idoneal discriminants $\\Delta$ and $\\Delta p^2$, for $p$ a prime. Employing this identity, we extend the results of Toh by writing the theta series of forms of discriminant $\\Delta p^2$ as a linear combination of Lambert series. We then use these Lambert series decompositions to give explicit representation formulas for the forms of discriminant $\\Delta p^2$. Lastly, we give a generalization of our main identity, which employs a map of Buell to connect forms of discriminant $\\Delta$ to $\\Delta "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6280","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":""},"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"}