{"id":"W2302953722","doi":"10.1007/s00013-017-1033-4","title":"The Fourier expansion of $$\\varvec{\\eta (z)\\eta (2z)\\eta (3z)/\\eta (6z)}$$ η ( z ) η ( 2 z ) η ( 3 z ) / η ( 6 z )","year":2017,"lang":"de","type":"article","venue":"Archiv der Mathematik","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Modular form; Fourier series; Integer (computer science); Section (typography); Modular design; Identity (music)","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":["metaresearch","metaepi_narrow","sts","scholarly_communication","open_science","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","insufficient_payload"],"category_scores_codex":[0.003702559,0.00182877,0.002956907,0.0004018803,0.003768178,0.001593345,0.005919912,0.0005897126,0.001166473],"category_scores_gemma":[0.01076729,0.001372689,0.001515194,0.000331159,0.003692923,0.001569979,0.00364362,0.001596367,0.003144101],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002005832,"about_ca_system_score_gemma":0.0004832484,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009580946,"about_ca_topic_score_gemma":0.0001364316,"domain_scores_codex":[0.9882532,0.0007225227,0.0038776,0.001675516,0.002953974,0.002517148],"domain_scores_gemma":[0.976186,0.007560724,0.004281488,0.01051245,0.0006953915,0.0007639003],"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":[0.0002792272,0.001609892,0.0001551862,0.00710103,0.002679611,0.0001952974,0.01467626,0.00002811955,0.002646289,0.9311026,0.03184293,0.007683562],"study_design_scores_gemma":[0.002017295,0.0002713887,0.0003690606,0.003100022,0.0016252,0.0001141576,0.002540519,0.004751532,0.007840787,0.9615363,0.01429253,0.001541242],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2491287,0.04471555,0.2490935,0.0215366,0.01660559,0.01931055,0.002027886,0.002340845,0.3952408],"genre_scores_gemma":[0.6041126,0.00948554,0.2175565,0.0004689728,0.003552386,0.0008530649,0.000149157,0.001882871,0.1619389],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.3549838,"threshold_uncertainty_score":0.9997466,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04991972136980451,"score_gpt":0.3331841671095168,"score_spread":0.2832644457397123,"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."}}