{"paper":{"title":"Zeta functions and the Fried conjecture for smooth pseudo-Anosov flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jonathan Zung, Malo J\\'ez\\'equel","submitted_at":"2024-09-25T15:17:14Z","abstract_excerpt":"To a transitive pseudo-Anosov flow $\\varphi$ on a $3$-manifold $M$ and a representation $\\rho$ of $\\pi_1(M)$, we associate a zeta function $\\zeta_{\\varphi,\\rho}(s)$ defined for $\\Re s \\gg 1$, generalizing the Anosov case. For a class of ``smooth pseudo-Anosov flows'', we prove that $\\zeta_{\\varphi,\\rho}(s)$ has a meromorphic continuation to $\\mathbb{C}$. We also prove a version of the Fried conjecture for smooth pseudo-Anosov flows which, under some conditions on $\\rho$, relates $\\zeta_{\\varphi,\\rho}(0)$ to the Reidemeister torsion of $M$. Finally we prove a topological analogue of the Dirichl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17014","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/2409.17014/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"}