{"id":"W4411230004","doi":"10.2140/ant.2025.19.1427","title":"Mean values of long Dirichlet polynomials with divisor coefficients","year":2025,"lang":"en","type":"article","venue":"Algebra & Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge; University of Northern British Columbia","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada; University of Northern British Columbia","keywords":"Mathematics; Dirichlet series; Dirichlet distribution; Divisor function; Divisor (algebraic geometry); Pure mathematics; Dirichlet L-function; Algebra over a field; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002263213,0.0003346109,0.0006756323,0.0002035904,0.0001753305,0.00005435845,0.000772416,0.0001365057,0.004990845],"category_scores_gemma":[0.001004065,0.000260363,0.0001879696,0.0007663091,0.0006962009,0.0001418373,0.0003564072,0.0003006074,0.0003106119],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009129986,"about_ca_system_score_gemma":0.0001894219,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002443003,"about_ca_topic_score_gemma":0.00003300849,"domain_scores_codex":[0.9969168,0.00071858,0.000602908,0.0004888349,0.0006711304,0.0006017539],"domain_scores_gemma":[0.9944404,0.003839695,0.0002453346,0.001070176,0.0002640483,0.0001403285],"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":[0.0005398349,0.0006174367,0.01250577,0.0003161936,0.0008126798,0.00003784666,0.001966233,0.000004533499,0.0001481753,0.9619832,0.0145427,0.006525415],"study_design_scores_gemma":[0.001089726,0.00008849299,0.001535745,0.0005023016,0.0003283906,0.00002329934,0.001826966,0.00006829193,0.01046581,0.9828493,0.0008265295,0.000395163],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8618228,0.0001640478,0.02995053,0.0001723694,0.000139277,0.00065082,0.00008595259,0.0001779003,0.1068363],"genre_scores_gemma":[0.9618884,0.000009465486,0.001369816,0.0001989946,0.00005919139,0.00003516703,0.00002015906,0.00007057811,0.03634824],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1000656,"threshold_uncertainty_score":0.9999849,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02302816383851993,"score_gpt":0.3305789204259336,"score_spread":0.3075507565874137,"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."}}