{"paper":{"title":"Averages and moments associated to class numbers of imaginary quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. R. Heath-Brown, L. B. Pierce","submitted_at":"2014-09-10T18:30:08Z","abstract_excerpt":"For any odd prime $\\ell$, let $h_\\ell(-d)$ denote the $\\ell$-part of the class number of the imaginary quadratic field $\\mathbb{Q}(\\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $\\ell =3$; nontrivial upper bounds for averages of $h_\\ell(-d)$ have previously been known only for $\\ell =3,5$. In this paper we prove nontrivial upper bounds for the average of $h_\\ell(-d)$ for all primes $\\ell \\geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $\\ell \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3177","kind":"arxiv","version":2},"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"}