{"id":"W2529139534","doi":"10.1017/s030500411700041x","title":"Traces, high powers and one level density for families of curves over finite fields","year":2017,"lang":"en","type":"preprint","venue":"Mathematical Proceedings of the Cambridge Philosophical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Mathematics; Finite field; Function field; Pure mathematics; Polynomial; Field (mathematics); Genus; Prime (order theory); Unitary matrix; Moduli; Function (biology); Riemann zeta function; Dirichlet distribution; Characteristic polynomial; Moduli space; Combinatorics; Mathematical analysis; Unitary state; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.002472238,0.0005313955,0.001734369,0.00005050145,0.0002889218,0.00009294544,0.001572505,0.0008402761,0.00003409303],"category_scores_gemma":[0.007147049,0.0003893036,0.001178798,0.0001180206,0.001914237,0.0001353083,0.00260586,0.001408722,0.000001912927],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009367773,"about_ca_system_score_gemma":0.0001472232,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003193585,"about_ca_topic_score_gemma":0.00000119507,"domain_scores_codex":[0.9964405,0.0000356647,0.001114682,0.0006888357,0.001207176,0.0005131302],"domain_scores_gemma":[0.9944513,0.002469694,0.001241508,0.0007897377,0.00084229,0.0002054324],"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":[0.00014577,0.000655078,0.0003236964,0.04440472,0.0009230704,4.547605e-7,0.0006825854,0.000001276869,0.0006700894,0.9398347,0.01223492,0.0001236784],"study_design_scores_gemma":[0.0006917204,0.00009400003,0.0006379456,0.00406059,0.0007156986,0.000005808069,0.0001481664,0.002323172,0.003060895,0.9878635,0.00001824415,0.0003802036],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9368297,0.0005275448,0.008673464,0.04084685,0.0002239436,0.004080712,0.001008783,0.0001233755,0.007685605],"genre_scores_gemma":[0.9786725,0.0003857706,0.01929531,0.0002568764,0.0002636378,0.0001085638,0.000008621667,0.0000858046,0.0009229105],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04802889,"threshold_uncertainty_score":0.9998559,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1243983570904419,"score_gpt":0.3438903130714237,"score_spread":0.2194919559809818,"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."}}