{"id":"W2618576910","doi":"10.1016/j.jnt.2018.07.005","title":"Moments of the error term in the Sato–Tate law for elliptic curves","year":2018,"lang":"en","type":"preprint","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"National Board for Higher Mathematics","keywords":"Mathematics; Elliptic curve; Central limit theorem; Cusp (singularity); Modular form; Identity (music); Modular group; Kronecker delta; Fist; Term (time); Distribution (mathematics); Limit (mathematics); Pure mathematics; Symmetry (geometry); Combinatorics; Mathematical analysis; Geometry; Statistics","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":[0.003321637,0.001190521,0.001671399,0.004414764,0.001293698,0.003251307,0.001904927,0.002303298,0.005842644],"category_scores_gemma":[0.02270024,0.0007739872,0.0008953101,0.002015688,0.005214921,0.005753325,0.002860685,0.003271475,0.0009178039],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0021258,"about_ca_system_score_gemma":0.0009262128,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001206906,"about_ca_topic_score_gemma":0.0007485403,"domain_scores_codex":[0.9988741,0.0003572128,0.00006507884,0.0001702918,0.0003454464,0.0001878113],"domain_scores_gemma":[0.9919052,0.003954425,0.001224688,0.0008295493,0.001168939,0.0009171828],"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":[0.0001206208,0.00002921915,0.0007649595,0.00006545206,0.00001960608,0.0001611397,0.0002723926,0.007005007,0.002023959,0.9836003,0.00111383,0.004823515],"study_design_scores_gemma":[0.0000256381,0.00004067353,0.00127307,0.00005857536,0.00002232885,0.0002360403,0.00008258765,0.08823194,0.001275271,0.9072522,0.001423934,0.00007782238],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.682186,0.003184894,0.2746303,0.004552501,0.0008739827,0.00005514308,0.0003423417,0.0006211267,0.03355374],"genre_scores_gemma":[0.9724849,0.0009035266,0.01191693,0.0002219574,0.00101383,0.00005414582,0.0001667332,0.0003203883,0.01291769],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005842644,"threshold_uncertainty_score":0.01954561,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.107422144265802,"score_gpt":0.4130956124424661,"score_spread":0.3056734681766641,"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."}}