{"paper":{"title":"Products of prime ideals in ray class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Likun Xie","submitted_at":"2026-06-29T17:09:28Z","abstract_excerpt":"We prove that every class in the narrow ray class group modulo an integral ideal $\\mathfrak q$ of a fixed number field is represented by a product of three prime ideals of norm at most $ ( N\\mathfrak q)^{\\max(1,3\\alpha,4\\alpha_0)+\\kappa} $ for any $\\kappa>0$, where $\\alpha$ is the exponent in short character sum bounds for general non-principal ray class characters and $\\alpha_0$ comes from a bounded-order subconvexity input for Hecke $L$-functions. Wu's subconvexity bound gives the admissible choice $\\alpha=\\alpha_0=103/256$, hence the explicit bound $(N\\mathfrak q)^{103/64+\\kappa}$. This imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30567","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/2606.30567/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"}