{"paper":{"title":"Erd\\H{o}s-Kac type theorem for the number of scattering geodesics on modular surface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.NT","authors_text":"Punya Plaban Satpathy, Sudhir Pujahari","submitted_at":"2025-06-09T06:49:43Z","abstract_excerpt":"In 1917, Hardy and Ramanujan showed that if $\\omega(n)$ is the number of distinct prime factors of a randomly chosen positive integer $n,$ then the normal order of $\\omega(n)$ is $\\log \\log \\, n.$ This led Erd\\H{o}s and Kac to prove their celebrated result showing a Gaussian behaviour for $\\omega(n).$ In this article we prove an Erd\\H{o}s-Kac kind result for the number of scattering geodesics on the modular surface with a common sojourn time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07474","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/2506.07474/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"}