{"id":"W2024555748","doi":"10.1016/j.jnt.2007.03.011","title":"Large gaps between the zeros of the Riemann zeta function","year":2007,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":23,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Ottawa","funders":"Natural Sciences and Engineering Research Council of Canada; Université de Montréal; National Science Foundation","keywords":"Mathematics; Riemann zeta function; Riemann hypothesis; Particular values of Riemann zeta function; Riemann Xi function; Explicit formulae; Arithmetic zeta function; Dirichlet distribution; Dirichlet series; Mathematical analysis; Function (biology); Prime zeta function; Polynomial; Pure mathematics; Dirichlet L-function","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":[],"category_scores_codex":[0.01417424,0.0001729905,0.0004174125,0.00008465492,0.0002245875,0.00003059185,0.000910375,0.0001254095,0.002620949],"category_scores_gemma":[0.001922581,0.00008614793,0.0004705742,0.0004168068,0.0003217129,0.0001654382,0.0002123787,0.0008530405,0.00008827972],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008749972,"about_ca_system_score_gemma":0.0001164676,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000209468,"about_ca_topic_score_gemma":0.000006063231,"domain_scores_codex":[0.9966892,0.0007926563,0.0009458229,0.0001225552,0.001030897,0.0004188928],"domain_scores_gemma":[0.9930798,0.004708297,0.0009812274,0.0006563358,0.0004534928,0.0001208164],"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":[0.0008049994,0.0004068966,0.04205487,0.0001631184,0.001094576,0.00003018464,0.002756996,0.000002308869,0.0008563329,0.9066343,0.0428962,0.002299184],"study_design_scores_gemma":[0.0006857103,0.00007731675,0.0142058,0.0001677422,0.0003468491,0.0001562994,0.002379826,0.000003256536,0.001931897,0.9665135,0.01342138,0.0001103847],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9020819,0.0002380304,0.05090374,0.0008740625,0.0006582799,0.0003941097,0.00006149532,0.00002447188,0.04476391],"genre_scores_gemma":[0.9933293,0.0000115085,0.000394433,0.0001677873,0.0007293128,0.000001360851,0.000001104977,0.00003919516,0.00532603],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09124737,"threshold_uncertainty_score":0.9982908,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04303870067144477,"score_gpt":0.3513727361197758,"score_spread":0.308334035448331,"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."}}