{"id":"W2330042366","doi":"10.4064/aa158-1-5","title":"Quadratic forms and a product-to-sum formula","year":2013,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Product (mathematics); Combinatorics; Quadratic equation; Gauss sum; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001179821,0.0006744598,0.000622982,0.001495072,0.001966882,0.002053793,0.001173521,0.001001375,0.009740924],"category_scores_gemma":[0.003936381,0.0004130006,0.0008851633,0.001342227,0.003809719,0.004637924,0.002865337,0.003129555,0.001573561],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001415235,"about_ca_system_score_gemma":0.0005948895,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001271111,"about_ca_topic_score_gemma":0.001018066,"domain_scores_codex":[0.9990991,0.0001695812,0.00004254626,0.0001598248,0.0003644925,0.000164549],"domain_scores_gemma":[0.998801,0.0004772284,0.00008867156,0.0001305085,0.000332271,0.0001702344],"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":[0.00001300762,0.00001135673,0.0001061018,0.00001651827,0.000003639826,0.00005570554,0.00009258337,0.0002649358,0.0004577244,0.9942907,0.001489709,0.003197955],"study_design_scores_gemma":[0.00001223382,0.0000210819,0.0002389821,0.00000784856,0.000007101351,0.0001305753,0.0000310845,0.004599539,0.0004568428,0.9907505,0.003733814,0.00001048498],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3641399,0.001927101,0.1647737,0.008321534,0.001366308,0.0000717306,0.000358388,0.000462854,0.4585784],"genre_scores_gemma":[0.9113161,0.0006089032,0.02492201,0.00124862,0.0009184845,0.00006229077,0.0002320573,0.0001813072,0.06051013],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009740924,"threshold_uncertainty_score":0.03258663,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03676501934409473,"score_gpt":0.3264151338057015,"score_spread":0.2896501144616068,"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."}}