{"id":"W2780963748","doi":"10.20903/csnmbs.masa.2017.38.2.111","title":"CONVERGENCE OF DIRICHLET SERIES AND EULER PRODUCTS","year":2017,"lang":"en","type":"article","venue":"Contributions Section of Natural Mathematical and Biotechnical Sciences","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Dirichlet series; Mathematics; Convergence (economics); Euler's formula; Dirichlet L-function; General Dirichlet series; Dirichlet conditions; Series (stratigraphy); Plane (geometry); Dirichlet distribution; Dirichlet kernel; Character (mathematics); Applied mathematics; Mathematical analysis; Geometry; Boundary value problem","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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","sts"],"consensus_categories":[],"category_scores_codex":[0.001230018,0.00009683438,0.0002972304,0.00005987665,0.0005009596,0.00005716207,0.0002790733,0.0001068335,0.00005163413],"category_scores_gemma":[0.008989728,0.00006110556,0.00004388428,0.0001992866,0.003308071,0.0002701275,0.0002482334,0.0001865736,0.000001715429],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001269655,"about_ca_system_score_gemma":0.00003842422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001330668,"about_ca_topic_score_gemma":0.000005387242,"domain_scores_codex":[0.998889,0.00005526554,0.0003213175,0.0002281732,0.0003170077,0.0001891874],"domain_scores_gemma":[0.9985604,0.0006220832,0.0002240806,0.0002521068,0.0002676883,0.00007369358],"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":[0.00003209606,0.00009178044,0.0004498439,0.0001982234,0.00001873007,7.581273e-7,0.00002734371,7.615143e-8,0.0361775,0.9622998,0.0001728848,0.0005309921],"study_design_scores_gemma":[0.0003025276,0.0003335016,0.005676184,0.0001906669,0.00005192751,0.00008476889,0.0001254399,0.0009197438,0.07770241,0.9141655,0.0002916913,0.0001556454],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9869339,0.0003233228,0.003575124,0.007510532,0.0001568919,0.0003479334,0.00003099981,0.00004514307,0.001076175],"genre_scores_gemma":[0.9954879,0.00008433186,0.004039875,0.000005339544,0.00003917513,0.00000498069,5.118051e-7,0.000002726981,0.0003351067],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04813428,"threshold_uncertainty_score":0.9994044,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05352958312309965,"score_gpt":0.372530580660161,"score_spread":0.3190009975370614,"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."}}