{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003718752,0.0009265852,0.001349603,0.004091315,0.001932662,0.004345395,0.002498317,0.001468975,0.006830534],"category_scores_gemma":[0.02358653,0.0008005622,0.0007571558,0.002241634,0.006177672,0.008597093,0.003022317,0.003299346,0.0008607453],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002154599,"about_ca_system_score_gemma":0.001009968,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004482184,"about_ca_topic_score_gemma":0.0004915323,"domain_scores_codex":[0.9985318,0.000472134,0.00004957872,0.0002701744,0.0003433352,0.0003328877],"domain_scores_gemma":[0.9833619,0.009805889,0.001699319,0.001177611,0.001528374,0.002426951],"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":[0.00006701043,0.00002425159,0.0005156684,0.00004818844,0.00001377299,0.00004677507,0.0001683738,0.001541904,0.001005354,0.9923441,0.0006279293,0.003596795],"study_design_scores_gemma":[0.00001138871,0.00001680862,0.0006911542,0.00002417631,0.000009036749,0.0001229939,0.00007206529,0.01104085,0.0006976998,0.9865954,0.0006862705,0.00003218419],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.697068,0.00217096,0.2479714,0.002664728,0.0005243433,0.00004238176,0.0003365149,0.0005744233,0.04864722],"genre_scores_gemma":[0.9767675,0.000717773,0.01382036,0.0002086369,0.0006360224,0.00006035304,0.000177854,0.0001666134,0.007444917],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006830534,"threshold_uncertainty_score":0.02285045,"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."}}