{"id":"W1537282355","doi":"10.4171/jems/757","title":"Large character sums: Burgess's theorem and zeros of $L$-functions","year":2017,"lang":"en","type":"preprint","venue":"Journal of the European Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Character (mathematics); Conjecture; Riemann hypothesis; Mathematics; Dirichlet distribution; Combinatorics; Critical line; Pure mathematics; Physics; Mathematical analysis; Geometry","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":[0.001472426,0.0006464974,0.0007595103,0.002557926,0.001621318,0.002890728,0.001160197,0.0008804183,0.005229211],"category_scores_gemma":[0.008828125,0.0003280331,0.0005524902,0.001078592,0.004482727,0.004415313,0.002883866,0.001560329,0.0006562337],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001056675,"about_ca_system_score_gemma":0.0003396515,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004882019,"about_ca_topic_score_gemma":0.0002987965,"domain_scores_codex":[0.9995812,0.0001361176,0.00001507857,0.00006782208,0.00009454587,0.0001052314],"domain_scores_gemma":[0.9970614,0.001628807,0.0003910613,0.0002080076,0.0002179856,0.0004926852],"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":[0.00006306328,0.00002284262,0.001355846,0.00004706647,0.00001220143,0.0001724104,0.0002783982,0.003067674,0.001406107,0.987571,0.001237835,0.004765565],"study_design_scores_gemma":[0.00002114368,0.00002873695,0.0007934773,0.00003460452,0.00001302689,0.0002505071,0.000141523,0.02895663,0.001400539,0.9667078,0.001629463,0.00002257836],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8967333,0.001407588,0.0557769,0.002765508,0.0001975254,0.00001737044,0.00009823884,0.0001696753,0.04283386],"genre_scores_gemma":[0.990364,0.0003679749,0.002865623,0.0001236456,0.0002057335,0.00002219503,0.00006131389,0.00003769318,0.005951796],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005229211,"threshold_uncertainty_score":0.01749343,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06656363268992112,"score_gpt":0.3429984739968123,"score_spread":0.2764348413068912,"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."}}