{"id":"W4205305890","doi":"10.1016/j.jnt.2017.09.022","title":"Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II","year":2017,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Arithmetic function; Ramanujan's sum; Mathematics; Convolution (computer science); Pure mathematics; Arithmetic; Algebra over a field; Discrete mathematics; Computer science","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.003129886,0.0001527514,0.0004746597,0.0001365461,0.0004926505,0.00006540053,0.000406409,0.0001339112,0.002619741],"category_scores_gemma":[0.006128317,0.0001198929,0.0001970432,0.00007775707,0.0007283946,0.0003210471,0.0002556706,0.0005057509,0.00003636384],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004922233,"about_ca_system_score_gemma":0.0001233499,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007912258,"about_ca_topic_score_gemma":0.000006337227,"domain_scores_codex":[0.9980331,0.0003935519,0.0006692503,0.0001451048,0.0005038509,0.0002551241],"domain_scores_gemma":[0.9955633,0.002418113,0.0007857251,0.0005793083,0.0004434544,0.0002100928],"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":[0.001411746,0.0008116341,0.01448569,0.0002073188,0.0008236172,0.0001376227,0.001754979,0.000003832398,0.001472845,0.9504441,0.02176947,0.006677123],"study_design_scores_gemma":[0.001472476,0.0002313926,0.006403772,0.0002991905,0.0002757865,0.0003706034,0.001292774,0.0003426415,0.0005343903,0.9860368,0.002570649,0.0001695005],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9592028,0.0001441295,0.0237127,0.0009030528,0.0003384375,0.00018262,0.00006277522,0.00001966162,0.01543385],"genre_scores_gemma":[0.9898313,0.00004900796,0.003827484,0.00003317014,0.0001999858,0.000002841374,0.0000023694,0.0000267624,0.006027135],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0355927,"threshold_uncertainty_score":0.998292,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06192286088836386,"score_gpt":0.3649671489451564,"score_spread":0.3030442880567925,"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."}}