{"paper":{"title":"Class number divisibility for imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Olivia Beckwith","submitted_at":"2018-09-15T17:51:45Z","abstract_excerpt":"In this note we revisit classic work of Soundararajan on class groups of imaginary quadratic fields. Let $A,B,g \\ge 3$ be positive integers such that $\\gcd(A,B)$ is square-free. We refine Soundararajan's result to show that if $4 \\nmid g$ or if $A$ and $B$ satisfy certain conditions, then the number of negative square-free $D \\equiv A \\pmod{B}$ down to $-X$ such that the ideal class group of $\\mathbb{Q} (\\sqrt{D})$ contains an element of order $g$ is bounded below by $X^{\\frac{1}{2} + \\epsilon(g) - \\epsilon}$, where the exponent is the same as in Soundararajan's theorem. Combining this with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05750","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"}