{"paper":{"title":"Erd\\H{o}s-Kac theorems for discriminants of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Jack B. Miller","submitted_at":"2026-06-05T17:34:54Z","abstract_excerpt":"The classical Erd\\H{o}s-Kac theorem gives a central limit theorem for the number of prime divisors of a random integer. We prove an analog for the number of ramified primes in a random $G$-extension of a number field when $G$ is abelian. This builds on previous work of Lemke Oliver and Thorne in the cases $G = S_d$ ($2 \\le d \\le 5$), and provides the first examples where local ramification events at distinct primes are not independent. We develop probability results that can be used \"out of the box\" to prove Erd\\H{o}s-Kac theorems for sequences of ideals in a number field, subject to Tauberian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07480","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/2606.07480/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"}