{"paper":{"title":"Explicit bounds for generators of the class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giuseppe Molteni, Lo\\\"ic Greni\\'e","submitted_at":"2016-07-08T15:54:54Z","abstract_excerpt":"Assuming Generalized Riemann's Hypothesis, Bach proved that the class group $\\mathcal C\\!\\ell_{\\mathbf K}$ of a number field ${\\mathbf K}$ may be generated using prime ideals whose norm is bounded by $12\\log^2\\Delta_{\\mathbf K}$, and by $(4+o(1))\\log^2\\Delta_{\\mathbf K}$ asymptotically, where $\\Delta_{\\mathbf K}$ is the absolute value of the discriminant of ${\\mathbf K}$. Under the same assumption, Belabas, Diaz y Diaz and Friedman showed a way to determine a set of prime ideals that generates $\\mathcal C\\!\\ell_{\\mathbf K}$ and which performs better than Bach's bound in computations, but which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02430","kind":"arxiv","version":5},"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"}