{"id":"W4221010321","doi":"10.1515/forum-2021-0171","title":"Sums of divisor functions and von Mangoldt convolutions in 𝔽<sub> <i>q</i> </sub>[<i>T</i>] leading to symplectic distributions","year":2022,"lang":"en","type":"article","venue":"Forum Mathematicum","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Divisor (algebraic geometry); Mathematics; Combinatorics; Symplectic geometry; Physics; Pure mathematics","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":[0.001757871,0.0007300013,0.0009419193,0.002775677,0.001700408,0.002415903,0.0009872782,0.0006962715,0.007172677],"category_scores_gemma":[0.005315084,0.000538849,0.001106143,0.001106775,0.003598012,0.003816749,0.001988154,0.001685627,0.0009498875],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002147841,"about_ca_system_score_gemma":0.0009654823,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00125909,"about_ca_topic_score_gemma":0.001450326,"domain_scores_codex":[0.9991559,0.000205084,0.00004702375,0.0001287702,0.0002783623,0.000184881],"domain_scores_gemma":[0.9980135,0.0008520893,0.0002406461,0.000176729,0.0003028306,0.0004142339],"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":[0.00002786734,0.0000153533,0.0002978884,0.0000230407,0.00000903226,0.0001790745,0.000196061,0.001452673,0.000595768,0.9932671,0.0007588234,0.003177425],"study_design_scores_gemma":[0.00001225975,0.00001773731,0.0005335908,0.0000185302,0.000009262161,0.0003005138,0.00007826604,0.0328379,0.001255099,0.9633557,0.001557257,0.0000240781],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.673103,0.001381354,0.2490067,0.00167958,0.000507804,0.00005664852,0.0002558942,0.0005127443,0.0734961],"genre_scores_gemma":[0.9623093,0.0003482437,0.01922809,0.0002062009,0.0002691966,0.00004513445,0.0001088444,0.0003015368,0.01718341],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007172677,"threshold_uncertainty_score":0.02399498,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03415807005694482,"score_gpt":0.303460906609531,"score_spread":0.2693028365525862,"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."}}