{"paper":{"title":"Prime geodesic theorem and closed geodesics for large genus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.NT","math.SP"],"primary_cat":"math.GT","authors_text":"Yuhao Xue, Yunhui Wu","submitted_at":"2022-09-21T15:04:07Z","abstract_excerpt":"Let $\\mathcal{M}_g$ be the moduli space of hyperbolic surfaces of genus $g$ endowed with the Weil-Petersson metric. In this paper, we show that for any $\\epsilon>0$, as $g\\to \\infty$, for a generic surface in $\\mathcal{M}_g$, the error term in the Prime Geodesic Theorem is bounded from above by $g\\cdot t^{\\frac{3}{4}+\\epsilon}$, up to a uniform constant multiplication. The expected value of the error term in the Prime Geodesic Theorem over $\\mathcal{M}_g$ is also studied. As an application, we show that as $g\\to \\infty$, on a generic hyperbolic surface in $\\mathcal{M}_g$ most closed geodesics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.10415","kind":"arxiv","version":3},"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/2209.10415/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"}