{"paper":{"title":"The distribution and density of cyclic groups of the reductions of an elliptic curve over a function field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M\\'arton Erd\\'elyi","submitted_at":"2016-09-20T09:29:13Z","abstract_excerpt":"Let $K$ be a global field of finite characteristic $p\\geq2$, and let $E/K$ be a non-isotrivial elliptic curve. We give an asympotoic formula of the number of places $\\nu$ for which the reduction of $E$ at $\\nu$ is a cyclic group. Moreover we determine when the Dirichlet density of those places is 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06066","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"}