{"id":"W2976827508","doi":"10.1112/plms.12546","title":"Multiplicative functions in short arithmetic progressions","year":2023,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Université du Québec à Montréal","funders":"HORIZON EUROPE Framework Programme; Academy of Finland; European Commission; University of Oxford","keywords":"Mathematics; Multiplicative function; Conjecture; Moduli; Arithmetic function; Prime number theorem; Discrete mathematics; Combinatorics; Arithmetic; Prime number; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001781165,0.0002017965,0.0004279454,0.00008024134,0.0001938999,0.00003951482,0.0006900685,0.0001509117,0.0001166374],"category_scores_gemma":[0.002303184,0.0001289301,0.0004199674,0.00179725,0.0004812797,0.0001273387,0.0005921827,0.0005195969,0.000125338],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001135709,"about_ca_system_score_gemma":0.00004253725,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002988825,"about_ca_topic_score_gemma":0.000001422883,"domain_scores_codex":[0.9978399,0.00001838652,0.0005670305,0.0003323351,0.0007354068,0.0005069819],"domain_scores_gemma":[0.9981679,0.001060211,0.0001073153,0.0002857915,0.0002639658,0.0001147731],"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":[0.00006981372,0.001975377,0.04857618,0.003428494,0.0004412053,0.000002228951,0.01466299,0.000008742278,0.02586752,0.8413554,0.0619664,0.001645684],"study_design_scores_gemma":[0.0004285089,0.00003636274,0.003310362,0.0004767266,0.00008425333,0.00001056219,0.005748696,0.01415191,0.007060562,0.9683149,0.0001668382,0.0002103528],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9865087,0.00001710001,0.0005522897,0.002451285,0.00003810972,0.001221254,0.00001244021,0.000242324,0.00895652],"genre_scores_gemma":[0.9823794,0.00001398098,0.01117088,0.00003899989,0.00005231789,0.0003652267,0.000001500703,0.00005723396,0.0059205],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1269595,"threshold_uncertainty_score":0.5257616,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06768019868486827,"score_gpt":0.3624247607748942,"score_spread":0.294744562090026,"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."}}