{"id":"W1628001501","doi":"10.1090/s0002-9939-02-06609-1","title":"On the number of Fourier coefficients that determine a Hilbert modular form","year":2002,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Modular form; Cusp form; Fourier series; Cusp (singularity); Quotient; Modular design; Fourier transform; Rayleigh quotient; Mathematical analysis; Pure mathematics; Physics; Geometry; Computer science; Quantum mechanics","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":[0.003595365,0.001270984,0.001435383,0.004055168,0.002456823,0.002514931,0.002102154,0.002152694,0.007246342],"category_scores_gemma":[0.02036424,0.0007589047,0.001359354,0.001368848,0.004330961,0.006905653,0.003110575,0.002782481,0.000976289],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009704202,"about_ca_system_score_gemma":0.000576712,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004056732,"about_ca_topic_score_gemma":0.0003675966,"domain_scores_codex":[0.9978294,0.0005379136,0.0001143085,0.0003614034,0.0008289752,0.0003280075],"domain_scores_gemma":[0.979856,0.01454016,0.001825699,0.00138619,0.001140489,0.001251403],"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":[0.001500888,0.0003765188,0.02141576,0.0006952338,0.0001797836,0.00164953,0.0008526823,0.02378235,0.04838016,0.836224,0.005130982,0.05981223],"study_design_scores_gemma":[0.0001764732,0.0002485212,0.01462778,0.0001923859,0.000234984,0.004403528,0.0004468556,0.22875,0.03498098,0.7114642,0.004231384,0.0002429176],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8095646,0.0008435199,0.1637946,0.001428674,0.0003348613,0.00006573915,0.0002956517,0.0002723879,0.02339992],"genre_scores_gemma":[0.9442407,0.0007847107,0.04517023,0.0001358413,0.0006018945,0.0001099814,0.0004955981,0.0001762325,0.008284858],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007246342,"threshold_uncertainty_score":0.02424145,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03174623554647936,"score_gpt":0.2828436324828446,"score_spread":0.2510973969363652,"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."}}