{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007806307,0.001141989,0.000717766,0.002553697,0.001241133,0.002476892,0.001009676,0.0007151909,0.007070578],"category_scores_gemma":[0.005137083,0.0004165997,0.0006547774,0.001208012,0.002172741,0.006840467,0.003983601,0.002900967,0.001560633],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009489187,"about_ca_system_score_gemma":0.0003247224,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002514099,"about_ca_topic_score_gemma":0.0003384966,"domain_scores_codex":[0.9988532,0.0001731472,0.00008519981,0.0002813459,0.0003827669,0.0002241655],"domain_scores_gemma":[0.9976522,0.0008863892,0.0003419832,0.0003523613,0.0004093776,0.0003576965],"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":[0.0002811525,0.00005440351,0.001755656,0.0002790883,0.00004496038,0.0004056873,0.0006005704,0.006193162,0.02378701,0.9282336,0.002588644,0.03577599],"study_design_scores_gemma":[0.00001738889,0.00009438309,0.00171517,0.0001003361,0.00007233091,0.0006674773,0.0001518262,0.02981166,0.02067431,0.9354864,0.01113989,0.00006887996],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5992086,0.003863641,0.2817049,0.001990623,0.001216306,0.00005308293,0.0002634331,0.0006120261,0.1110874],"genre_scores_gemma":[0.9614431,0.001091162,0.02338972,0.0004025187,0.0008389498,0.00007144966,0.0001708112,0.0002586594,0.01233367],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007070578,"threshold_uncertainty_score":0.02365339,"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."}}