{"id":"W2101367141","doi":"10.1112/s0024611504015175","title":"Integral moments of L-functions","year":2005,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":410,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Arithmetic function; Symplectic geometry; Random matrix; Order (exchange); Interpretation (philosophy); Matrix (chemical analysis); Unitary state; Pure mathematics; Unitary matrix; Algebra over a field; Mathematical analysis; Eigenvalues and eigenvectors","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.001126714,0.0001705226,0.0004245468,0.00003094482,0.0001060383,0.00002094792,0.0006683288,0.0001154147,0.0005304684],"category_scores_gemma":[0.001073954,0.0001061797,0.0005694194,0.000404517,0.0004460406,0.0001593811,0.0003526312,0.0003309048,0.00004956056],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001010603,"about_ca_system_score_gemma":0.00003173489,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002728977,"about_ca_topic_score_gemma":4.338213e-7,"domain_scores_codex":[0.9981269,0.000009394939,0.0006037527,0.0001938646,0.0007494008,0.0003166528],"domain_scores_gemma":[0.9985689,0.0004086915,0.0003312591,0.0002332857,0.0003681181,0.00008973684],"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":[0.00004097594,0.00100291,0.002448231,0.001615688,0.0003670982,5.572463e-8,0.003709265,0.000002068438,0.01942842,0.9275489,0.0429908,0.0008455293],"study_design_scores_gemma":[0.0005685208,0.0000545142,0.0001308942,0.0002783476,0.0001632515,0.00001087324,0.002397144,0.003176376,0.05214351,0.9402409,0.0006807543,0.0001549431],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9660158,0.0000286197,0.002230081,0.00202877,0.00003784831,0.0005207892,0.00001154246,0.00006741252,0.0290592],"genre_scores_gemma":[0.9526426,0.000008938299,0.0346187,0.00006293369,0.00008928714,0.00003003121,3.898708e-7,0.00003599807,0.01251114],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04231005,"threshold_uncertainty_score":0.5808256,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03950083489494447,"score_gpt":0.3216119916678347,"score_spread":0.2821111567728902,"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."}}