{"id":"W4385606001","doi":"10.1142/s1793042123501233","title":"Fourier coefficients of automorphic L-functions","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Cusp form; Modular form; Zero (linguistics); Hecke operator; Cusp (singularity); Asymptotic formula; Automorphic form; Fourier series; Prime (order theory); Modular group; Combinatorics; Pure mathematics; Mathematical analysis; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002740764,0.0001174658,0.0002730275,0.0003902426,0.00004823823,0.00003066107,0.0007591736,0.000067552,0.009465006],"category_scores_gemma":[0.002711756,0.00009817964,0.0002676884,0.0004010707,0.0002016249,0.000163456,0.0001622163,0.00030142,0.000719091],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001023986,"about_ca_system_score_gemma":0.0001627061,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003031664,"about_ca_topic_score_gemma":0.000001334739,"domain_scores_codex":[0.9974465,0.0002669634,0.0006871028,0.0001157352,0.001274781,0.0002088993],"domain_scores_gemma":[0.9956888,0.002254923,0.000517096,0.0002269997,0.001204543,0.0001076392],"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":[0.000910654,0.0008366439,0.007345739,0.00006053765,0.002302878,0.0005895811,0.001644202,0.0002622869,0.001153686,0.7372599,0.2349868,0.01264715],"study_design_scores_gemma":[0.001202132,0.00007538915,0.001132813,0.0002414177,0.00009862668,0.0005083003,0.001114747,0.000917482,0.0006930002,0.9733996,0.02046154,0.0001549458],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8925217,0.00003420034,0.05261807,0.00138366,0.003083885,0.0002044289,0.0003523785,0.0001177291,0.04968391],"genre_scores_gemma":[0.9769469,0.00001623529,0.00144922,0.00006675675,0.0004063795,0.000003963324,0.00001517981,0.00003609166,0.02105922],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2361397,"threshold_uncertainty_score":0.9914405,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06215158253351223,"score_gpt":0.3897463875515872,"score_spread":0.327594805018075,"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."}}