{"id":"W4396867843","doi":"10.1007/s00209-024-03496-7","title":"A weighted one-level density of the non-trivial zeros of the Riemann zeta-function","year":2024,"lang":"en","type":"article","venue":"Mathematische Zeitschrift","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Riemann hypothesis; Riemann zeta function; Pure mathematics; Function (biology); Particular values of Riemann zeta function; Arithmetic zeta function; Mathematical analysis; Prime zeta function","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":[0.002064044,0.001104595,0.001533019,0.00483542,0.001762567,0.003877565,0.002920731,0.002112239,0.007166191],"category_scores_gemma":[0.008950919,0.0009108746,0.001077519,0.00145599,0.004388885,0.004717648,0.003034469,0.002052644,0.001009552],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001293934,"about_ca_system_score_gemma":0.0006190856,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007215542,"about_ca_topic_score_gemma":0.000700599,"domain_scores_codex":[0.9991229,0.0002332905,0.00003661824,0.0001512553,0.0002556359,0.0002004312],"domain_scores_gemma":[0.9962554,0.001381591,0.0004609731,0.0005147998,0.000510221,0.0008770487],"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":[0.0001401877,0.00008913525,0.001426558,0.0001377407,0.00003221391,0.0003277769,0.0002396599,0.004641456,0.005095817,0.9822091,0.001068031,0.00459247],"study_design_scores_gemma":[0.00004669561,0.00004676602,0.002403299,0.00006908809,0.0000349315,0.0005336228,0.0001406431,0.1011922,0.001779269,0.8928728,0.000803146,0.00007770094],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7751563,0.0008175456,0.1835049,0.001358587,0.0003905277,0.00006300437,0.0002111555,0.0007059374,0.03779202],"genre_scores_gemma":[0.9771065,0.0003944022,0.01031623,0.0002912775,0.0003263762,0.00008810969,0.0001880141,0.0002520614,0.01103706],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007166191,"threshold_uncertainty_score":0.02397323,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06861052520107376,"score_gpt":0.3142906035171228,"score_spread":0.2456800783160491,"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."}}