{"id":"W2606596439","doi":"10.1112/s0025579317000225","title":"SMOOTH‐SUPPORTED MULTIPLICATIVE FUNCTIONS IN ARITHMETIC PROGRESSIONS BEYOND THE ‐BARRIER","year":2017,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"H2020 European Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Multiplicative function; Multiplicative inverse; Moduli; Arithmetic function; Arithmetic progression; Algebra over a field","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003101852,0.0009352205,0.001410651,0.003219649,0.001238692,0.004004597,0.001868126,0.001180894,0.00599206],"category_scores_gemma":[0.02561061,0.0004523637,0.0009577696,0.00171332,0.004036003,0.008248591,0.003726868,0.002886829,0.001116067],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001254946,"about_ca_system_score_gemma":0.0007801095,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004785939,"about_ca_topic_score_gemma":0.0003021049,"domain_scores_codex":[0.9983802,0.0003949227,0.00007093781,0.0004099178,0.0004303004,0.0003138408],"domain_scores_gemma":[0.9867353,0.006775287,0.002137009,0.001930446,0.001214838,0.001206986],"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":[0.0001584589,0.00003427536,0.001702054,0.00009765584,0.00003583921,0.0001492614,0.0002880856,0.0077688,0.003080443,0.9757711,0.001087119,0.009826825],"study_design_scores_gemma":[0.00002506516,0.00008290682,0.00186597,0.00003879033,0.00002993371,0.0003194644,0.0001260592,0.04694877,0.001881357,0.9466174,0.002018558,0.00004572651],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6927037,0.001562151,0.283232,0.001781606,0.0002122893,0.00004506885,0.0003785102,0.0006660175,0.01941868],"genre_scores_gemma":[0.9842387,0.0005245726,0.01058322,0.0001377753,0.0002754317,0.00006156071,0.000154912,0.00008197812,0.003941896],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00599206,"threshold_uncertainty_score":0.0200454,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07868092075379558,"score_gpt":0.3896217169074644,"score_spread":0.3109407961536688,"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."}}