{"paper":{"title":"Quadratic Irrationals, Closed Geodesics on the Modular Surface and Dynamical Zeta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.NT","authors_text":"Peter Hazard","submitted_at":"2018-05-03T17:05:40Z","abstract_excerpt":"We show that generating functions associated to the sequence of convergents of a quadratic irrational are related in a natural way to the dynam- ical zeta function of a hyperbolic automorphism of the 2-torus. As a corollary, this shows that the L\\'evy constant of a quadratic irrational appears naturally as the topological entropy of such maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01429","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":""},"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"}