{"paper":{"title":"Neumann scalar determinants on constant curvature disks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Soumyadeep Chaudhuri","submitted_at":"2025-07-07T16:14:43Z","abstract_excerpt":"Working in the $\\zeta$-function regularisation scheme, we find certain infinite series representations of the logarithms of massive scalar determinants, $\\det(\\Delta+m^{2})$ for arbitrary $m^2$, on finite round disks of constant curvature ($R=\\frac{2\\eta}{L^2}, \\eta=0,\\pm1$) with Neumann boundary conditions. The derivation of these representations relies on a relation between the Neumann determinants on the disks and the corresponding Dirichlet determinants via the determinants of the Dirichlet-to-Neumann maps on the boundaries of the disks. We corroborate the results in an appendix by computi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05159","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}