{"paper":{"title":"An inequality for the zeta function of a planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexandre Jollivet, Vladimir Sharafutdinov","submitted_at":"2015-10-22T09:40:19Z","abstract_excerpt":"We consider the zeta function $\\zeta\\_\\Omega$ for the Dirichlet-to-Neumann operator of a simply connected planar domain $\\Omega$ bounded by a smooth closed curve.We prove non-negativeness and growth properties for $\\zeta\\_\\Omega(s)-2\\big({L(\\partial \\Omega)\\over 2\\pi}\\big)^s\\zeta\\_R(s)\\ (s\\leq-1)$, where $L(\\partial \\Omega)$ is the length of the boundary curve and $\\zeta\\_R$ stands for the classical Riemann zeta function.Two analogs of these results are also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06548","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"}