{"id":"W2801998207","doi":"10.1016/j.jmaa.2018.04.071","title":"Explicit zero density for the Riemann zeta function","year":2018,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University; University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Zero (linguistics); Riemann zeta function; Riemann hypothesis; Generalization; Function (biology); Riemann Xi function; Explicit formulae; Constant (computer programming); Upper and lower bounds; Particular values of Riemann zeta function; Pure mathematics; Mathematical analysis; Combinatorics; Arithmetic zeta function; Prime zeta function","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001885964,0.0001114501,0.0004151767,0.0001539825,0.0003673273,0.00007702467,0.0002710351,0.00005568807,0.0002754003],"category_scores_gemma":[0.0004737471,0.00006253877,0.000371183,0.0006325065,0.0002054488,0.00008019711,0.00006180615,0.0001526338,0.00003099162],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002273734,"about_ca_system_score_gemma":0.00002680885,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001974992,"about_ca_topic_score_gemma":0.00001081566,"domain_scores_codex":[0.998673,0.00005529761,0.0005945854,0.000144253,0.000359386,0.0001735211],"domain_scores_gemma":[0.9961856,0.002279966,0.0003767469,0.0003931851,0.0006398834,0.0001246091],"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":[0.00005486919,0.0002246556,0.000246188,0.00006314437,0.001817785,3.928948e-7,0.0001847643,0.000002265652,0.0002910176,0.9906028,0.002809478,0.003702634],"study_design_scores_gemma":[0.0002053962,0.00009016493,0.0003968627,0.00001341152,0.003852771,0.00002389589,0.0003306189,0.00553327,0.000256177,0.9855185,0.003702741,0.00007619683],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0213431,0.0000627737,0.9761188,0.001252431,0.00001178041,0.0003102594,0.00000465149,0.00001027149,0.0008859163],"genre_scores_gemma":[0.971659,0.00003380513,0.02628455,0.0001185571,0.0004849297,0.00008325926,0.000001503158,0.0000164635,0.001317946],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9503159,"threshold_uncertainty_score":0.301544,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0602588703591501,"score_gpt":0.3620716208876695,"score_spread":0.3018127505285194,"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."}}