{"id":"W4243710577","doi":"10.1016/j.jnt.2015.09.023","title":"On the error term in a Parseval type formula in the theory of Ramanujan expansions II","year":2015,"lang":"en","type":"article","venue":"Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Mathematics; Ramanujan's sum; Arithmetic function; Parseval's theorem; Term (time); Convolution (computer science); Type (biology); Pure mathematics; Asymptotic formula; Asymptotic expansion; Discrete mathematics; Mathematical analysis; Fourier analysis; Fourier transform","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.01744736,0.0001998214,0.0004733004,0.0002140456,0.00008990809,0.00002810856,0.001070373,0.000114645,0.001690611],"category_scores_gemma":[0.006172268,0.00009904441,0.0002144712,0.0004749674,0.0003094076,0.0001622199,0.0001695497,0.0009932388,0.00007703665],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001347293,"about_ca_system_score_gemma":0.0003018183,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000055155,"about_ca_topic_score_gemma":0.00002879044,"domain_scores_codex":[0.9950152,0.002650402,0.000872886,0.0001421327,0.0009456024,0.0003737915],"domain_scores_gemma":[0.9899812,0.008458774,0.0005011453,0.0006560727,0.0002877552,0.0001150417],"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":[0.001991676,0.0009309506,0.001315744,0.00003142111,0.0001128885,0.000152974,0.01990378,0.00002724738,0.0001398624,0.9603834,0.01388065,0.001129398],"study_design_scores_gemma":[0.001136801,0.0003099643,0.0007022193,0.0002812445,0.00005278995,0.0002282627,0.01787122,0.00005532313,0.0001411541,0.9784944,0.0006130292,0.0001135687],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9742109,0.00007036195,0.0002441262,0.001006633,0.0001470178,0.0003299051,0.000009428762,0.000006718965,0.02397489],"genre_scores_gemma":[0.9973126,0.00001140244,0.0003459622,0.000355751,0.0001159235,0.00001002072,0.000001047944,0.00003343764,0.001813873],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02310166,"threshold_uncertainty_score":0.999222,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1547795549918101,"score_gpt":0.3963079432775583,"score_spread":0.2415283882857481,"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."}}