{"id":"W2152115950","doi":"10.1142/s1793042113500620","title":"THE NON-CYCLOTOMIC PART OF f(x)x<sup>n</sup>+ g(x) AND ROOTS OF RECIPROCAL POLYNOMIALS OFF THE UNIT CIRCLE","year":2013,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Northern British Columbia","funders":"","keywords":"Mathematics; Cyclotomic polynomial; Reciprocal; Combinatorics; Unit circle; Unit (ring theory); Polynomial; Degree (music); Discriminant; Zero (linguistics); Bounded function; Factorization; Prime (order theory); Irreducible polynomial; Root of unity; Mathematical analysis; Physics","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":[0.0004593073,0.0005049548,0.0003328758,0.000663153,0.0008415807,0.001588964,0.000423713,0.000522486,0.00460824],"category_scores_gemma":[0.00263098,0.0002004044,0.000420994,0.0004104543,0.00307571,0.001719554,0.001216701,0.001483825,0.0008292086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007251201,"about_ca_system_score_gemma":0.0003223268,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005576536,"about_ca_topic_score_gemma":0.0005674877,"domain_scores_codex":[0.9996096,0.0000720184,0.00001997424,0.00009782814,0.0001240945,0.00007649243],"domain_scores_gemma":[0.9991397,0.0003150645,0.0002108649,0.0001565333,0.00008119539,0.00009669973],"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":[0.000133319,0.00002171132,0.0009403168,0.00006035346,0.000004316409,0.0003711935,0.0003264125,0.003855773,0.005443436,0.9788941,0.0006831806,0.009265873],"study_design_scores_gemma":[0.00002862365,0.0001552242,0.003129568,0.00004809435,0.00002691514,0.002068981,0.0003208595,0.04439443,0.01744734,0.9210462,0.01128209,0.00005156716],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7586372,0.0007254013,0.128269,0.0008329007,0.0001515724,0.00002401536,0.0001071116,0.0002377621,0.1110151],"genre_scores_gemma":[0.9848023,0.0002082819,0.009767932,0.00003648459,0.00009380125,0.000006796132,0.00003780924,0.00002791561,0.005018584],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00460824,"threshold_uncertainty_score":0.01541609,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0173464107725081,"score_gpt":0.2877020185804769,"score_spread":0.2703556078079689,"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."}}