{"id":"W1985589545","doi":"10.1017/s0013091508000771","title":"Bilinear character sums and sum-product problems on elliptic curves","year":2010,"lang":"en","type":"article","venue":"Proceedings of the Edinburgh Mathematical Society","topic":"Cryptography and Residue Arithmetic","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"University of Waterloo","keywords":"Character (mathematics); Bilinear interpolation; Multiplicative function; Mathematics; Finite field; Product (mathematics); Bilinear form; Elliptic curve; Pure mathematics; Discrete mathematics; Mathematical analysis; Statistics; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.0009320939,0.0002059217,0.0002919502,0.00003483115,0.0001919952,0.0001289159,0.0009577627,0.0001034047,0.00004567053],"category_scores_gemma":[0.0003236891,0.0001193721,0.000283039,0.0004980452,0.0004269665,0.0003152975,0.000414095,0.0005321152,0.000005085524],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007884189,"about_ca_system_score_gemma":0.00002059541,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002121949,"about_ca_topic_score_gemma":1.761675e-7,"domain_scores_codex":[0.9983827,0.000004780879,0.0003393135,0.0004276963,0.0005193956,0.0003261256],"domain_scores_gemma":[0.9989865,0.0001850448,0.0001901163,0.0003273361,0.0001937557,0.0001172158],"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":[0.00001932381,0.001812287,0.01249154,0.005349006,0.0003377855,8.290311e-7,0.01054457,0.000003175892,0.2951948,0.6074377,0.05971995,0.007089037],"study_design_scores_gemma":[0.001626771,0.0005429458,0.01782619,0.003677325,0.0002996704,0.0001877202,0.0004789133,0.04078295,0.2157327,0.706418,0.01077779,0.001649073],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9825767,0.0003087574,0.0008470269,0.01240997,0.0005809622,0.0007691738,0.000002689605,0.0001647622,0.002339946],"genre_scores_gemma":[0.966702,0.0003630015,0.03108429,0.0007558194,0.0004280766,0.00005606729,4.517077e-7,0.00002406166,0.000586235],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09898026,"threshold_uncertainty_score":0.4867854,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01025887474955521,"score_gpt":0.2182147829559103,"score_spread":0.2079559082063552,"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."}}