{"id":"W2083492767","doi":"10.4064/aa137-3-6","title":"On the logarithmic derivatives of Dirichlet L-functions at s=1","year":2009,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":41,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Chuo University","keywords":"Mathematics; Logarithm; Dirichlet distribution; Pure mathematics; Mathematical analysis","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":[0.003066909,0.002086446,0.001278507,0.007842424,0.002945464,0.00533999,0.002828129,0.002493494,0.0115249],"category_scores_gemma":[0.01470555,0.0007277732,0.0009282173,0.002889371,0.007734378,0.008024969,0.003551765,0.004628277,0.00193201],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003994774,"about_ca_system_score_gemma":0.001377338,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001445389,"about_ca_topic_score_gemma":0.001082647,"domain_scores_codex":[0.9989617,0.0003873865,0.00004556,0.0001340609,0.0002489047,0.0002224087],"domain_scores_gemma":[0.9955923,0.001788899,0.0005638068,0.0002852483,0.0006035528,0.00116629],"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":[0.0001108917,0.00003441471,0.0003521638,0.00006139429,0.000007087317,0.000144048,0.0003589284,0.001913558,0.001125971,0.9896473,0.001151183,0.005093077],"study_design_scores_gemma":[0.0000303934,0.00002619115,0.0007868875,0.00006030435,0.000009496162,0.0001981188,0.0001424905,0.01644263,0.0006382601,0.9797909,0.001831956,0.00004244677],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6018319,0.005264996,0.1105553,0.01127976,0.001667457,0.0000823737,0.0003174198,0.0008491143,0.2681516],"genre_scores_gemma":[0.9494393,0.002236651,0.009242958,0.0007107408,0.001161743,0.00006098564,0.0002392361,0.0003654661,0.03654297],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0115249,"threshold_uncertainty_score":0.03855461,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05648449539050098,"score_gpt":0.3359148681833921,"score_spread":0.2794303727928911,"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."}}