{"id":"W4402997304","doi":"10.1112/mtk.12281","title":"A discrete mean value of the Riemann zeta function","year":2024,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Lethbridge","funders":"Natural Sciences and Engineering Research Council of Canada; Austrian Science Fund; Agence Nationale de la Recherche; Pacific Institute for the Mathematical Sciences; University of Lethbridge","keywords":"Mathematics; Riemann zeta function; Pure mathematics; Value (mathematics); Riemann hypothesis; Riemann Xi function; Mathematical analysis; Statistics","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":[0.00246837,0.0009484876,0.001019486,0.003529003,0.0007270038,0.00280272,0.001633266,0.0009916943,0.004463667],"category_scores_gemma":[0.01256708,0.0003402664,0.0006830023,0.0007881059,0.004261048,0.004159788,0.002640823,0.002562579,0.0006037172],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001341546,"about_ca_system_score_gemma":0.000698661,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004301329,"about_ca_topic_score_gemma":0.0003253517,"domain_scores_codex":[0.9991424,0.0002665693,0.00003531208,0.0001543331,0.0002687259,0.0001326708],"domain_scores_gemma":[0.9931768,0.003993007,0.0005733056,0.0005851648,0.0009562346,0.0007154589],"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":[0.0001235864,0.00006956006,0.002952868,0.000224819,0.00005748886,0.000309156,0.0001449115,0.01394099,0.01127719,0.9621131,0.001216801,0.007569658],"study_design_scores_gemma":[0.00001839815,0.00007812271,0.003071709,0.0001485941,0.00004851989,0.0004208229,0.0001123973,0.3465943,0.01004184,0.6367162,0.002673928,0.0000752134],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4625654,0.003017734,0.4921381,0.002478241,0.0005713256,0.00002983463,0.0001489035,0.0004718372,0.03857853],"genre_scores_gemma":[0.9776094,0.0006318801,0.01574417,0.0001583121,0.0004516179,0.00002616436,0.00009453146,0.0001143414,0.005169585],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004463667,"threshold_uncertainty_score":0.01493245,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04328213145676837,"score_gpt":0.3386189098392238,"score_spread":0.2953367783824555,"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."}}