{"id":"W1991052404","doi":"10.1134/s0001434610090312","title":"Character sums over shifted primes","year":2010,"lang":"en","type":"article","venue":"Mathematical Notes","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":19,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Multiplicative function; Modulo; Character (mathematics); Integer (computer science); Combinatorics; Upper and lower bounds; Range (aeronautics); 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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001040635,0.0002466671,0.0004370221,0.00009903758,0.0001039184,0.0001141537,0.0004427176,0.0001973261,0.01246239],"category_scores_gemma":[0.00551341,0.0001821429,0.0001675767,0.0002002439,0.0002891797,0.0001557625,0.0001953465,0.0006434814,0.00239862],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000020722,"about_ca_system_score_gemma":0.00004645759,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005211475,"about_ca_topic_score_gemma":0.00001037232,"domain_scores_codex":[0.9980211,0.00007883373,0.0004487715,0.0003203032,0.0005988875,0.0005321236],"domain_scores_gemma":[0.9949611,0.00379006,0.00009558484,0.0008166382,0.00009773042,0.000238903],"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":[0.00002129437,0.0004007253,0.00161354,0.0002006427,0.00006452492,0.00001949081,0.0004436067,2.05132e-8,0.01049938,0.9845651,0.001064887,0.001106805],"study_design_scores_gemma":[0.0003196896,0.00002785013,0.001859465,0.0000512744,0.0000466911,0.00003037703,0.00002990231,0.0009170717,0.009021197,0.9860693,0.001373692,0.0002535132],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9671321,0.000005712818,0.007042516,0.001018994,0.0001165016,0.0003775036,0.000008364133,0.0002528157,0.02404548],"genre_scores_gemma":[0.9556766,0.000001200663,0.03914946,0.0001678513,0.000295007,0.00004219714,0.000004940783,0.00008114427,0.00458158],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03210694,"threshold_uncertainty_score":0.9983781,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05063521960221752,"score_gpt":0.3620850349835646,"score_spread":0.3114498153813471,"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."}}