{"id":"W1804349709","doi":"10.1007/s00208-016-1482-2","title":"Sums of Euler products and statistics of elliptic curves","year":2016,"lang":"en","type":"article","venue":"Mathematische Annalen","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal; Concordia University","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Euler's formula; Product (mathematics); Elliptic curve; Range (aeronautics); Connection (principal bundle); Euler characteristic; Field (mathematics); Supersingular elliptic curve","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":[0.003803444,0.00102061,0.001559334,0.006431079,0.001382423,0.005334512,0.001569252,0.001071757,0.004473482],"category_scores_gemma":[0.01549501,0.0008545752,0.0006965652,0.004018795,0.005470393,0.009255425,0.003394203,0.001786912,0.0004938853],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001487786,"about_ca_system_score_gemma":0.0007182176,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004865746,"about_ca_topic_score_gemma":0.0003643811,"domain_scores_codex":[0.9985884,0.0004787207,0.000108197,0.0002633143,0.0003838177,0.0001775102],"domain_scores_gemma":[0.9879908,0.007781768,0.001703779,0.000591954,0.000782817,0.001148829],"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":[0.00004442519,0.00001707888,0.001702179,0.00003757896,0.00001468942,0.00004119617,0.0002251023,0.002319617,0.0003638616,0.9902374,0.0004418286,0.004554941],"study_design_scores_gemma":[0.000004915478,0.00001076744,0.0009819994,0.00001671187,0.00000901511,0.00009031009,0.00006353599,0.006087455,0.0002263678,0.9917186,0.0007747029,0.00001559724],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8357189,0.004299365,0.1348596,0.001936145,0.000233118,0.00002347322,0.0004471631,0.0001755684,0.02230674],"genre_scores_gemma":[0.9809342,0.002431144,0.008493195,0.000123386,0.0007210732,0.00004832244,0.0004266316,0.00009002448,0.006732012],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006431079,"threshold_uncertainty_score":0.02011478,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08317037864242145,"score_gpt":0.3468159122723453,"score_spread":0.2636455336299239,"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."}}