{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004145725,0.0002416013,0.0005607109,0.00001909683,0.0001512145,0.00002072888,0.0006968317,0.00005816248,0.0004262001],"category_scores_gemma":[0.001254955,0.0001251996,0.0005483797,0.0006146617,0.000841544,0.00009451577,0.0002544672,0.0002619291,0.00003470898],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004657847,"about_ca_system_score_gemma":0.000005930653,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001419712,"about_ca_topic_score_gemma":6.274227e-8,"domain_scores_codex":[0.9981961,0.000008921399,0.0004383236,0.0002365208,0.0007606263,0.0003595504],"domain_scores_gemma":[0.997636,0.001014702,0.0007555966,0.0003519453,0.0001665211,0.00007521598],"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":[0.00004648212,0.001700213,0.003383885,0.001072069,0.0003846928,4.096091e-7,0.006833163,0.00000504892,0.003803378,0.9593194,0.01958991,0.003861358],"study_design_scores_gemma":[0.0003142357,0.00009393991,0.0003058047,0.0002484723,0.000115634,0.00001556418,0.001751244,0.007698487,0.01150108,0.9775903,0.0001472403,0.0002179551],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9853274,0.000009116711,0.002287231,0.001071995,0.00002601968,0.0003943972,0.000008212314,0.00004081589,0.01083484],"genre_scores_gemma":[0.9774294,0.00001491276,0.02101596,0.0005372927,0.00003228039,0.00003425174,1.510714e-7,0.00004112182,0.0008946251],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01944267,"threshold_uncertainty_score":0.5105491,"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."}}