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Using the superzeta function approach due to Voros, we define a Hurwitz-type zeta function $\\zeta^{\\pm}_{B}(s,z)$ constructed from the resonances associated to $zI -[ (1/2)I \\pm B]$. We prove the meromorphic continuation in $s$ of $\\zeta^{\\pm}_{B}(s,z)$ and, using the special value at $s=0$, define a determinant of the operators $zI -[ (1/2)I \\pm B]$. We obtain expressions for Selberg's zeta function and the determinant of the scattering matrix in terms "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.07613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T15:04:50Z","cross_cats_sorted":["math-ph","math.CV","math.MP","math.SP"],"title_canon_sha256":"bcd6d1adb7cad6c2f540d1ca5027f6234b4b2d91ea2cf7d2c3c662132264faa2","abstract_canon_sha256":"e129f75a7c63ae8a2d2108c0c23d65895b5f559bc15e56494847db54eb644ac0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:20.379755Z","signature_b64":"r56fhgmzrA3My8G8Biz5BeVzHdbBaku8qCUVcqlsyxta3EGpADnOaFTtED7vXjWK/UdCmRG0Lp6AIYCEV19WCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff6cb289b54f270997b992895b385b6cf15176f844ce3f203ac1f734045c7af","last_reissued_at":"2026-05-18T01:18:20.379051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:20.379051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The determinant of the Lax-Phillips scattering operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP","math.SP"],"primary_cat":"math.NT","authors_text":"Jay Jorgenson, Joshua S. Friedman, Lejla Smajlovic","submitted_at":"2016-03-24T15:04:50Z","abstract_excerpt":"Let $M$ denote a finite volume, non-compact Riemann surface without elliptic points, and let $B$ denote the Lax-Phillips scattering operator. Using the superzeta function approach due to Voros, we define a Hurwitz-type zeta function $\\zeta^{\\pm}_{B}(s,z)$ constructed from the resonances associated to $zI -[ (1/2)I \\pm B]$. We prove the meromorphic continuation in $s$ of $\\zeta^{\\pm}_{B}(s,z)$ and, using the special value at $s=0$, define a determinant of the operators $zI -[ (1/2)I \\pm B]$. 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