{"id":"W4408782862","doi":"10.4153/s0008439525000335","title":"Shifted moments of quadratic Dirichlet <i>L</i> -functions","year":2025,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Dirichlet distribution; Quadratic equation; Pure mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0008368716,0.0002066166,0.0004870709,0.0004036003,0.00014553,0.0000409965,0.000439904,0.0001412536,0.02284947],"category_scores_gemma":[0.002877295,0.000188437,0.0001506295,0.0006331264,0.0002685161,0.0000263048,0.00007967225,0.0002702518,0.005148042],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002496371,"about_ca_system_score_gemma":0.0004650834,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000675579,"about_ca_topic_score_gemma":0.001001014,"domain_scores_codex":[0.9980092,0.0001559213,0.0006243965,0.0002829896,0.0003617056,0.0005657938],"domain_scores_gemma":[0.9972347,0.001349252,0.0000923404,0.0006974186,0.0001740001,0.0004522797],"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":[0.00001295057,0.0001562541,0.0002139434,0.000470702,0.0001422464,0.00001933634,0.0001617451,0.00000101159,0.00006066408,0.7947816,0.2037396,0.0002399683],"study_design_scores_gemma":[0.0004580094,0.00003644575,0.00007992986,0.0003207108,0.0001269914,0.000008056067,0.0004967088,0.0003639754,0.0002680754,0.9451469,0.05248496,0.0002092138],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1746845,0.0001132182,0.04040616,0.01882182,0.0002135727,0.001380204,0.00012176,0.0001700329,0.7640887],"genre_scores_gemma":[0.860062,0.000003834118,0.004951298,0.0007997879,0.0000396255,0.0001036307,0.00001275741,0.00004983896,0.1339772],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6853775,"threshold_uncertainty_score":0.9956266,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02861038272293895,"score_gpt":0.3150216192930296,"score_spread":0.2864112365700906,"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."}}