{"paper":{"title":"On the minima of positive definite binary hamiltonian forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Fr\\'ed\\'eric Paulin (LM-Orsay), Ga\\\"etan Chenevier (LMO)","submitted_at":"2019-05-13T06:55:18Z","abstract_excerpt":"Let $A$ be a definite quaternion algebra over $\\mathbb Q$, with discriminant $D_A$, and $O$ a maximal order of $A$. We show that the minimum of the positive definite hamiltonian binary forms over $O$ with discrimiminant $-1$ is $\\sqrt{D_A}$. When the different of $O$ is principal, we provide an explicit form representing this minimum, and when $O$ is principal, we give the list of the equivalence classes of all such forms. We also give criteria and algorithms to determine when the different of $O$ is principal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04881","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"}