{"paper":{"title":"Coset Diagram for the Action of Picard Group on Q(i,\\surd3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Qaiser Mushtaq, Saima Anis","submitted_at":"2011-11-16T12:17:49Z","abstract_excerpt":"The Picard group {\\Gamma} is PSL(2,Z[i]). We have defined coset diagram for the Picard group. It has been observed that some elements of Q(i,/surd3) of the form ((a+b/surd3)/c) and their conjugates ((a-b/surd3)/c) over \\mathbb{Q}(i) have different signs in the coset diagram for the action of {\\Gamma} on the biquadratic field Q(i,/surd3), these are called ambiguous numbers. We have noticed that ambiguous numbers in the coset diagram for the action of {\\Gamma} on \\mathbb{Q}(i,/surd3) form a unique pattern. It has been shown that there are finite number of ambiguous numbers in an orbit {\\Gamma}{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3778","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"}