{"paper":{"title":"Boundary CM points and class groups of small exponent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Aiken, Dmitriy Shvydkoy, Erick Ross, Hui Xue","submitted_at":"2026-05-25T16:40:51Z","abstract_excerpt":"Let $\\mathcal F$ denote the fundamental domain for $\\text{SL}_2(\\mathbb{Z})$ on the upper half plane $\\mathcal H$. William Duke showed that as fundamental discriminants $D \\to -\\infty$, the sets $\\mathrm{CM}_{D}$ (CM points of discriminant $D$) are equidistributed in $\\mathcal F$. In this paper, we investigate the behavior of CM points on the boundary of $\\mathcal F$. We prove that such CM points are equidistributed on the boundary, and also give a complete characterization of when every $\\mathrm{CM}_D$ point lies on the boundary. Along the way, we also (conditionally) give a complete classifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26020","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/2605.26020/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"}