{"paper":{"title":"Distribution of squarefree values of sequences associated with elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chantal David, Heekyoung Hahn, Lola Thompson, Shabnam Akhtari","submitted_at":"2012-10-12T05:30:22Z","abstract_excerpt":"Let E be a non-CM elliptic curve defined over Q. For each prime p of good reduction, E reduces to a curve E_p over the finite field F_p. For a given squarefree polynomial f(x,y), we examine the sequences f_p(E) := f(a_p(E), p), whose values are associated with the reduction of E over F_p. We are particularly interested in two sequences: f_p(E) =p + 1 - a_p(E) and f_p(E) = a_p(E)^2 - 4p. We present two results towards the goal of determining how often the values in a given sequence are squarefree. First, for any fixed curve E, we give an upper bound for the number of primes p up to X for which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3433","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"}