{"id":"W2040923100","doi":"10.1016/j.aam.2013.04.001","title":"Identities for the Ramanujan zeta function","year":2013,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Ramanujan's sum; Mathematics; Riemann zeta function; Hypergeometric function; Ramanujan tau function; Pure mathematics; Hypergeometric distribution; Arithmetic zeta function; Algebraic number; Combinatorics; Algebra over a field; Mathematical analysis","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":[0.002331682,0.001277651,0.001035078,0.004790427,0.002560637,0.004848443,0.001659705,0.001624282,0.008300692],"category_scores_gemma":[0.005401134,0.0005202048,0.001153807,0.001755192,0.004148704,0.00623381,0.003124984,0.004803405,0.003454512],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002038252,"about_ca_system_score_gemma":0.001276906,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001261542,"about_ca_topic_score_gemma":0.0008117739,"domain_scores_codex":[0.9988362,0.0003276307,0.00006220798,0.0001451904,0.0005024698,0.0001263719],"domain_scores_gemma":[0.9983662,0.0005912196,0.0001491689,0.0002156374,0.0004172366,0.0002605259],"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":[0.00000397336,0.000006347596,0.00003672349,0.0000114664,0.000002046247,0.00001912088,0.00006728587,0.000164053,0.0002102693,0.9967148,0.0007425222,0.002021447],"study_design_scores_gemma":[0.000003879173,0.000002768605,0.00005537981,0.000009335954,0.000001807186,0.0000342351,0.00001941337,0.001337372,0.00009909136,0.996316,0.002113231,0.000007564266],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1671188,0.009767782,0.3278202,0.007880194,0.003954984,0.0001081832,0.0005975892,0.0004714979,0.482281],"genre_scores_gemma":[0.8476171,0.006686269,0.04770516,0.001662231,0.005385814,0.0002372965,0.0006082975,0.0003913096,0.08970641],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008300692,"threshold_uncertainty_score":0.02776855,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03046188669035829,"score_gpt":0.3147266089888871,"score_spread":0.2842647222985288,"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."}}