{"paper":{"title":"Holomorphic factorization of determinants of Laplacians using quasi-Fuchsian uniformization","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrew Mcintyre, Lee-Peng Teo","submitted_at":"2006-05-23T04:37:47Z","abstract_excerpt":"For a quasi-Fuchsian group $\\Ga$ with ordinary set $\\Omega$, and $\\Delta_{n}$ the Laplacian on \\n differentials on $\\Ga\\bk\\Omega$, we define a notion of a Bers dual basis $\\phi_{1},...c,\\phi_{2d}$ for $\\ker\\Delta_{n}$. We prove that $\\det\\Delta_{n}/\\det <\\phi_{j},\\phi_{k}>$, is, up to an anomaly computed by Takhtajan and the second author in \\cite{TT1}, the modulus squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta Z(n). This generalizes the D'Hoker-Phong formula $\\det\\Delta_{n}=c_{g,n}Z(n)$, and is a quasi-Fuchsian counterpart of the result for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605605","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"}