{"id":"W2323102738","doi":"10.5802/aif.2035","title":"Non-vanishing of class group <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>L</mml:mi> </mml:math> -functions at the central point","year":2004,"lang":"lv","type":"article","venue":"Annales de l’institut Fourier","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Class (philosophy); Mathematics; Quadratic equation; Constant (computer programming); Group (periodic table); Point (geometry); Combinatorics; Pure mathematics; Mathematical physics; Mathematical analysis; Physics; Geometry; Quantum mechanics; Computer science","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":[0.001273223,0.0011131,0.001162271,0.002938375,0.003295859,0.00430088,0.001597371,0.001555263,0.0202464],"category_scores_gemma":[0.004860189,0.000495074,0.001158748,0.0006930986,0.004202938,0.005729011,0.002678046,0.004273653,0.003758267],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003477748,"about_ca_system_score_gemma":0.001863686,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002814545,"about_ca_topic_score_gemma":0.002128151,"domain_scores_codex":[0.9986567,0.0001948426,0.0000370058,0.000335166,0.0002839094,0.0004923127],"domain_scores_gemma":[0.9971846,0.0004908711,0.0003291168,0.0003214435,0.0005381708,0.001135735],"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":[0.0001595534,0.00006270454,0.0007020665,0.00006302277,0.00001574956,0.0002439011,0.0002908912,0.000489172,0.002191186,0.9821003,0.005401203,0.008280219],"study_design_scores_gemma":[0.0000701368,0.0001081564,0.001799482,0.00004354033,0.00002082089,0.0004778068,0.0002205638,0.0102419,0.003675925,0.9741173,0.009169661,0.00005468879],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5759902,0.001173115,0.1512174,0.006038072,0.002177738,0.0001148427,0.0005971011,0.002015335,0.2606761],"genre_scores_gemma":[0.9171665,0.0004793122,0.01000524,0.0005497879,0.001180039,0.00009875604,0.0003945814,0.0007403667,0.06938532],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0202464,"threshold_uncertainty_score":0.0677309,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01943372093335908,"score_gpt":0.249494261001456,"score_spread":0.2300605400680969,"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."}}