{"paper":{"title":"Spectral gaps on thick part of moduli spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.GT","math.NT","math.SP"],"primary_cat":"math.DG","authors_text":"Haohao Zhang, Yunhui Wu","submitted_at":"2025-01-16T03:31:37Z","abstract_excerpt":"In this paper, we study spectral gaps of closed hyperbolic surfaces for large genus. We show that for any fixed $k\\geq 1$, as the genus goes to infinity, the maximum of $\\lambda_k-\\lambda_{k-1}$ over any thick part of the moduli space of closed Riemann surfaces approaches the limit $\\frac{1}{4}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09266","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/2501.09266/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"}