{"id":"W1968781015","doi":"10.1080/10586458.2004.10504532","title":"On the Vanishing of Twisted<i>L</i>-Functions of Elliptic Curves","year":2004,"lang":"en","type":"article","venue":"Experimental Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":37,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"","keywords":"Mathematics; Elliptic curve; Conjecture; Dirichlet distribution; Order (exchange); Cubic function; Combinatorics; Function (biology); Pure mathematics; Mathematical analysis","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":[0.0006646384,0.000175069,0.0003650397,0.00006696416,0.00009182539,0.00001446663,0.0004095475,0.00005145276,0.0006584238],"category_scores_gemma":[0.0007488093,0.0001185514,0.0001716117,0.0002561663,0.0002966609,0.00007429216,0.0001214758,0.0001831896,0.00008884678],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009322,"about_ca_system_score_gemma":0.00005527454,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001317468,"about_ca_topic_score_gemma":0.000001781648,"domain_scores_codex":[0.9983331,0.00007109011,0.0005695365,0.0001571369,0.0006477702,0.0002213783],"domain_scores_gemma":[0.9975423,0.001347068,0.0002965396,0.0006691262,0.00008608188,0.00005890373],"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":[0.00001504735,0.001276454,0.000007120952,0.0005192926,0.00009556064,0.000002391062,0.003438769,0.00002237521,0.02716213,0.9661077,0.001344404,0.000008810008],"study_design_scores_gemma":[0.0004367314,0.000241595,0.000003690374,0.001192017,0.00005373832,0.0000168355,0.007759929,0.0001663676,0.4228616,0.567102,0.00002649473,0.0001390324],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9471429,0.0005594953,0.01215354,0.0004521528,0.0001134545,0.0007811486,0.00002219406,0.00006796326,0.03870713],"genre_scores_gemma":[0.9913682,0.00001626242,0.007529441,0.00008109245,0.00002366098,0.00003493727,0.000002086755,0.0000405379,0.0009037494],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3990057,"threshold_uncertainty_score":0.7209279,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0756290386451961,"score_gpt":0.3568150565858846,"score_spread":0.2811860179406885,"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."}}