{"paper":{"title":"The multiplicative anomaly of three or more commuting elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Eduardo Friedman, Marius Mantoiu, Victor Castillo-Garate","submitted_at":"2012-11-17T12:25:16Z","abstract_excerpt":"Zeta-regularized determinants are well-known to fail to be multiplicative. Hence one is lead to study the n-fold multiplicative anomaly M_n(A_1,...,A_n) :=\\frac{\\det_\\zeta\\Big(\\prod_{i=1}^n A_i\\Big)}{\\prod_{i=1}^n \\det_\\zeta(A_i)} attached to n (suitable) operators A_1,...,A_n. We show that if the A_i are commuting pseudo-differential elliptic operators, then their joint multiplicative anomaly can be expressed in terms of the pairwise multiplicative anomalies. Namely M_n(A_1,...,A_n)^{m_1+...+m_n} =\\prod_{1\\le i<j\\le n}M_2(A_i,A_j)^{m_i+m_j}, where m_j is the order of A_j. The proof relies on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4117","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"}