{"paper":{"title":"The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexey Kokotov, Dmitrii Korikov","submitted_at":"2026-08-10T15:35:45Z","abstract_excerpt":"Let $(M,g)$ be a smooth orientable $2d$ Riemannian manifold of genus $\\mathfrak{g}$ with Riemannian metric $g$ and connected boundary $\\Gamma$. Let $\\Lambda$ be the Dirichlet-to-Neumann map on $\\Gamma$ and let ${\\rm det}_\\zeta(\\Lambda)$ be its (modified, i. e. with zero mode excluded) $\\zeta$-regularized determinant. It is well-known that the quantity ${\\rm det}_\\zeta(\\Lambda)/|\\Gamma|$ (where $|\\Gamma|$ is the length of $\\Gamma$) is a conformal invariant. It was shown by Edward and Wu (\\cite{EV}) that this invariant equals one for $\\mathfrak{g}=0$; in the case $\\mathfrak{g}>0$ Guillarmou and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09737","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/2608.09737/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"}