{"id":"W1970377478","doi":"10.1142/s1793042113500140","title":"NONZERO VALUES OF DIRICHLET L-FUNCTIONS IN VERTICAL ARITHMETIC PROGRESSIONS","year":2013,"lang":"en","type":"preprint","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge; University of British Columbia","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Arithmetic progression; Mathematics; Dirichlet series; Conjecture; Function (biology); Zero (linguistics); Arithmetic function; Dirichlet distribution; Arithmetic; Dirichlet L-function; Analytic number theory; Combinatorics; Upper and lower bounds; Rational number; Pure mathematics; Discrete mathematics; 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":[0.001530592,0.001129673,0.0007907207,0.003177174,0.001868167,0.003793192,0.001170638,0.0007146475,0.005937224],"category_scores_gemma":[0.008985208,0.0004902614,0.0006681618,0.001221477,0.005185793,0.003654335,0.002922005,0.001951473,0.000984838],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001721095,"about_ca_system_score_gemma":0.0006924437,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005811352,"about_ca_topic_score_gemma":0.0005004537,"domain_scores_codex":[0.9989875,0.0002286757,0.00005865679,0.000200538,0.0002101518,0.000314332],"domain_scores_gemma":[0.9956499,0.001916136,0.0006849617,0.0003104477,0.0005261007,0.000912407],"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":[0.000730288,0.00007631906,0.0069931,0.0002494469,0.000030557,0.0006810043,0.0007635878,0.007746228,0.01880731,0.9430873,0.00118828,0.01964649],"study_design_scores_gemma":[0.0001065905,0.0002137042,0.004828565,0.0001894454,0.00004892198,0.0009683426,0.0007195126,0.03052649,0.01602961,0.9405701,0.005670272,0.0001284452],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9194662,0.0007709086,0.0490337,0.0005580328,0.00009704534,0.00002916888,0.0001779561,0.0001901491,0.02967696],"genre_scores_gemma":[0.9850121,0.0003618084,0.008094135,0.00004331918,0.0001096463,0.00004996674,0.0002325848,0.00005357506,0.006042893],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005937224,"threshold_uncertainty_score":0.019862,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0581562815653314,"score_gpt":0.4042029761591408,"score_spread":0.3460466945938094,"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."}}