{"id":"W2050062132","doi":"10.1142/s1793042107001036","title":"ODD VALUES OF FOURIER COEFFICIENTS OF CERTAIN MODULAR FORMS","year":2007,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Modular form; Hecke operator; Coprime integers; Conjecture; Eigenvalues and eigenvectors; Pure mathematics; Siegel modular form; Fourier series; Operator (biology); Value (mathematics); Eisenstein series; Cusp form; Combinatorics; Mathematical analysis; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007846764,0.0005541309,0.0003456003,0.001504413,0.0007569917,0.001305349,0.0005925343,0.0005080882,0.005721912],"category_scores_gemma":[0.003382118,0.0002739971,0.0002709471,0.0005431178,0.001820193,0.001602234,0.0008416942,0.0007128834,0.0003283184],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008031486,"about_ca_system_score_gemma":0.0003514589,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004389696,"about_ca_topic_score_gemma":0.0006045048,"domain_scores_codex":[0.9997287,0.00005381335,0.00001213317,0.00003670647,0.00006117615,0.0001073809],"domain_scores_gemma":[0.9990012,0.0004438142,0.0002018711,0.00008954141,0.00009317612,0.0001704926],"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":[0.0005650446,0.0001474378,0.00972904,0.0001353786,0.00003097209,0.001239479,0.0007894927,0.006284722,0.02399025,0.9340721,0.002009079,0.02100704],"study_design_scores_gemma":[0.0001416919,0.0001584838,0.01184408,0.0001002107,0.00005165423,0.00123953,0.0006752844,0.06671567,0.01723057,0.8958378,0.005903097,0.0001019615],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9766269,0.0001100313,0.008340039,0.0001933588,0.00004924444,0.000009348229,0.00006095136,0.0000481631,0.01456193],"genre_scores_gemma":[0.993971,0.00007475744,0.00236217,0.00002642009,0.00004930673,0.00001311768,0.00005044554,0.00002366744,0.003429273],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005721912,"threshold_uncertainty_score":0.01914173,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01959796861099924,"score_gpt":0.3515327657404728,"score_spread":0.3319347971294736,"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."}}