{"paper":{"title":"Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pradipto Banerjee, Srinivas Kotyada","submitted_at":"2011-02-18T07:24:24Z","abstract_excerpt":"In this paper we find a new lower bound on the number of imaginary quadratic extensions of the function field $\\mathbb{F}_{q}(x)$ whose class groups have elements of a fixed odd order. More precisely, for $q$, a power of an odd prime, and $g$ a fixed odd positive integer $\\ge 3$, we show that for every $\\epsilon >0$, there are $\\gg q^{L(1/2+\\frac{3}{2(g+1)}-\\epsilon)}$ polynomials $f \\in \\mathbb{F}_{q}[x]$ with $\\deg f=L$, for which the class group of the quadratic extension $\\mathbb{F}_{q}(x, \\sqrt{f})$ has an element of order $g$. This sharpens the previous lower bound $q^{L(1/2+\\frac{1}{g})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3769","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"}