{"paper":{"title":"Niveau de r\\'epartition des polyn\\^omes quadratiques et crible majorant pour les entiers friables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"R\\'egis de la Bret\\`eche, Sary Drappeau","submitted_at":"2017-03-09T09:41:38Z","abstract_excerpt":"We obtain new estimates on the level of distribution of the set $\\{Q(n)\\}$ where $Q\\in{\\mathbb Z}[X]$ is irreducible quadratic, for well-factorable moduli, improving a result due to Iwaniec. As a by-product of our arguments, we study the Chebyshev problem of estimating $\\max\\{P^+(n^2-D), n\\leq x\\}$ and make explicit, in Deshouillers-Iwaniec's state-of-the-art result, the dependence on the Selberg eigenvalue conjecture. Combined with the construction of an upper-bound sieve for numbers free of large factors, we obtain new upper bounds for the quantity $\\Psi_Q(x, y) = |\\{n\\leq x: p\\mid Q(n)\\Righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03197","kind":"arxiv","version":3},"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"}