{"paper":{"title":"Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.SP","authors_text":"Anke Pohl, Ksenia Fedosova","submitted_at":"2017-09-03T19:30:57Z","abstract_excerpt":"We initiate the study of Selberg zeta functions $Z_{\\Gamma,\\chi}$ for geometrically finite Fuchsian groups $\\Gamma$ and finite-dimensional representations $\\chi$ with non-expanding cusp monodromy. We show that for all choices of $(\\Gamma,\\chi)$, the Selberg zeta function $Z_{\\Gamma,\\chi}$ converges on some half-plane in $\\mathbb{C}$. In addition, under the assumption that $\\Gamma$ admits a strict transfer operator approach, we show that $Z_{\\Gamma,\\chi}$ extends meromorphically to all of $\\mathbb{C}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00760","kind":"arxiv","version":4},"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/1709.00760/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"}