{"id":"W1801982364","doi":"10.1090/s0002-9939-00-06021-4","title":"Trigonometric polynomials with many real zeros and a Littlewood-type problem","year":2000,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Trigonometric polynomial; Unimodular matrix; Trigonometry; Flatness (cosmology); Polynomial; Pure mathematics; Type (biology); Discrete mathematics; Combinatorics; Mathematical analysis; Physics","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":[],"consensus_categories":[],"category_scores_codex":[0.0008029658,0.000339451,0.000954492,0.00005939227,0.0002271367,0.00009954802,0.0004395966,0.00009202762,0.0006321362],"category_scores_gemma":[0.0003632236,0.0001954139,0.0003066814,0.001397568,0.000912921,0.0001614841,0.0001424759,0.0002782757,0.0000322089],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000611998,"about_ca_system_score_gemma":0.00004847325,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003232661,"about_ca_topic_score_gemma":3.480236e-7,"domain_scores_codex":[0.9978948,0.00002214658,0.0007341289,0.0003918838,0.0004852474,0.0004717438],"domain_scores_gemma":[0.9979454,0.0007988749,0.000570495,0.0003021029,0.0001843222,0.0001988078],"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":[0.0009428589,0.002691193,0.007504405,0.006101218,0.001486745,0.000001220445,0.009565376,0.000003030267,0.01602987,0.8819955,0.04946277,0.02421581],"study_design_scores_gemma":[0.002111219,0.001791097,0.004262562,0.0009411062,0.001173746,0.0002030951,0.003614632,0.001510661,0.00885242,0.9705397,0.003685253,0.001314493],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9620636,0.00003503473,0.0002145858,0.0008127071,0.00001531218,0.0007963315,0.00001164968,0.0001179126,0.03593283],"genre_scores_gemma":[0.8159337,0.000318275,0.1763375,0.0003082153,0.0001582273,0.0001163589,8.200013e-7,0.0001046291,0.006722312],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1761229,"threshold_uncertainty_score":0.7968749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01998799053935668,"score_gpt":0.2666682709603996,"score_spread":0.2466802804210429,"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."}}