{"paper":{"title":"A short note on the divisibility of class numbers of real quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jaitra Chattopadhyay","submitted_at":"2018-04-23T03:16:27Z","abstract_excerpt":"For any integer $l\\geq 1$, let $p_1, p_2, \\ldots, p_{l+2}$ be distinct prime numbers $\\geq 5.$ For all real numbers $X>1,$ we let $N_{3,l}(X)$ denote the number of real quadratic fields $K$ whose absolute discriminant $d_K\\leq X$ and $d_K$ is divisible by $(p_1\\ldots p_{l+2})$ together with the class number $h_K$ of $K$ divisible by $2^{l}\\cdot 3.$ Then, in this short note, by following the method in \\cite{Byeonkoh}, we prove that $N_{3,l}(X) \\gg X^\\frac{7}{8}$ for all large enough $X$'s."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08235","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"}