{"id":"W2081086511","doi":"10.1007/s00208-007-0101-7","title":"Primes in quadratic progressions on average","year":2007,"lang":"en","type":"article","venue":"Mathematische Annalen","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto; Queen's University","funders":"","keywords":"Mathematics; Quadratic equation; Prime number theorem; Discrete mathematics; Prime number; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003054815,0.0009975961,0.002091365,0.004648196,0.003593126,0.006120495,0.002200198,0.001650109,0.02014478],"category_scores_gemma":[0.01852715,0.0009633706,0.0009964254,0.003306477,0.005720572,0.01282081,0.004052422,0.003925925,0.001915929],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002869688,"about_ca_system_score_gemma":0.00131195,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001284706,"about_ca_topic_score_gemma":0.001113671,"domain_scores_codex":[0.9978819,0.0004919408,0.00009586253,0.0004748464,0.0005387357,0.0005166587],"domain_scores_gemma":[0.9868326,0.008225843,0.001296702,0.001022471,0.0008882475,0.001734023],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000127137,0.00003075284,0.0004177322,0.00003833657,0.00000716946,0.00007773508,0.0003286663,0.001548919,0.0003967034,0.9921916,0.001214173,0.003621104],"study_design_scores_gemma":[0.00002366981,0.0000217614,0.0003580739,0.00001380848,0.000008708539,0.00008748509,0.0000661122,0.004382547,0.0002681597,0.9938048,0.0009507916,0.00001401885],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7896761,0.001676706,0.09679855,0.005272284,0.0004941724,0.00008513446,0.0005083279,0.0008818235,0.1046069],"genre_scores_gemma":[0.9720042,0.0006545281,0.006443388,0.0003684801,0.0005758233,0.00007863057,0.0001983561,0.0002000736,0.01947653],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02014478,"threshold_uncertainty_score":0.06739104,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08804707661823984,"score_gpt":0.4065328459285155,"score_spread":0.3184857693102757,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}