{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001359631,0.0005135961,0.0008529046,0.001460412,0.0007132136,0.001749626,0.0007586599,0.000461385,0.001772525],"category_scores_gemma":[0.009591236,0.0002085271,0.0004543032,0.0007439747,0.002283041,0.002358993,0.001536687,0.00138054,0.0002740726],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006993511,"about_ca_system_score_gemma":0.000294157,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001878078,"about_ca_topic_score_gemma":0.0001104629,"domain_scores_codex":[0.9990188,0.000234143,0.00005144974,0.0001867206,0.0003659257,0.0001429748],"domain_scores_gemma":[0.9971694,0.00166356,0.0004919008,0.0002256708,0.0002000301,0.0002493511],"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":[0.0003228477,0.0000803997,0.005032607,0.0001253997,0.00006174119,0.0005101181,0.0005310248,0.0267597,0.01303336,0.9313571,0.0007723382,0.02141324],"study_design_scores_gemma":[0.00004522072,0.0001947593,0.004299155,0.00007167567,0.0000488697,0.0007628021,0.0002546349,0.1039644,0.01187337,0.8741831,0.004245714,0.00005630332],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.929234,0.0006083795,0.05638169,0.0003218693,0.00005925611,0.00001289608,0.00004897241,0.00009475026,0.01323811],"genre_scores_gemma":[0.9939809,0.0001336234,0.004775598,0.00002449945,0.00008550112,0.00001544937,0.00003881608,0.00001993153,0.0009256648],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001772525,"threshold_uncertainty_score":0.007190466,"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."}}